Neutron Stars in Alternative Theories of Gravity
|
|
|
- Carmel Poole
- 6 years ago
- Views:
Transcription
1 .. Neutron Stars in Alternative Theories of Gravity Jutta Kunz Institute of Physics CvO University Oldenburg NewCompStar School 2017 Neutron stars: theory, observations and gravitational waves emission Sofia, September 2017 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
2 . Outline Outline. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
3 . Outline Outline. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
4 . Outline Outline. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
5 . Outline Outline. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
6 . Outline Outline. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
7 . Outline Motivation. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
8 . Motivation Motivation General Relativity G µν + Λg µν = 8πT µν In four spacetime dimensions the only divergence-free symmetric rank-2 tensor constructed solely from the metric and its derivatives up to second differential order, is the Einstein tensor plus a cosmological term. Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
9 . Motivation Motivation General Relativity Compatible with all solar system observations Compatible with all astrophysical observations New Observations in the strong gravity regime? Black holes Neutron stars Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
10 . Motivation Motivation General Relativity Incompatibility with Quantum Mechanics Singularities Dark Matter, Dark Energy Future Observations? Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
11 Motivation. Motivation GR or Alternative Theories of Gravity Scalar-tensor theories f (R) theories Higher curvature theories Massive gravity... Jutta Kunz (Universita t Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
12 . Motivation Motivation GR or Alternative Theories of Gravity Scalar-tensor theories f(r) theories Higher curvature theories Massive gravity... Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
13 . Motivation Motivation Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
14 . Outline Neutron Stars in General Relativity. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
15 Neutron Stars in General Relativity. Neutron Stars in General Relativity Demorest et al., Nature 476, 1081 (2010) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
16 Neutron Stars in General Relativity. Neutron Stars in General Relativity Cipolletta et al., arxiv: : RMF Static sequence Keplerian sequence f =50 Hz f =200 Hz f =300 Hz f =500 Hz f =716 Hz M [M ] R eq [km] Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
17 Neutron Stars in General Relativity. Neutron Stars in General Relativity Cipolletta et al., arxiv: : RMF M [M ] Static sequence Keplerian sequence Secular Instability f =50 Hz f =200 Hz f =300 Hz f =500 Hz f =716 Hz log(ε c /c 2 [g cm 3 ]) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
18 Neutron Stars in General Relativity. Neutron Stars in General Relativity Cipolletta et al., arxiv: : RMF energy density contours: ϵ c = g/cm 3 static rotating Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
19 Neutron Stars in General Relativity. Neutron Stars in General Relativity Cipolletta et al., arxiv: : RMF 5 4 Keplerian sequence f =50 Hz f =200 Hz f =300 Hz f =500 Hz f =716 Hz I [10 45 g cm 2 ] M [M ] Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
20 . Outline Neutron Stars in Scalar-Tensor Theories. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
21 . Outline Neutron Stars in Scalar-Tensor Theories STT. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
22 Neutron Stars in Scalar-Tensor Theories. Scalar-Tensor Theories STT action: Jordan frame 1 S = d 4 x g 16πG G : gravitational constant R: Ricci scalar with respect to g µν Φ: graviational scalar field S m : matter action Ψ m : matter fields [ F (Φ) R ] Z(Φ) g µν µ Φ ν Φ 2U(Φ) + S m [Ψ m ; g µν ] Φ does not couple directly to Ψ m : weak equivalence principle is satisfied Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
23 Neutron Stars in Scalar-Tensor Theories. Scalar-Tensor Theories STT action: Jordan frame 1 S = d 4 x g 16πG [ F (Φ) R ] Z(Φ) g µν µ Φ ν Φ 2U(Φ) + S m [Ψ m ; g µν ] functions F (Φ) and Z(Φ), and potential function U(Φ) physical restrictions positivity of the graviton energy: F (Φ) > 0 positivity of the scalar field kinetic energy: ( ) 2 d 2F (Φ)Z(Φ) + 3 dφ F (Φ) 0 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
24 Neutron Stars in Scalar-Tensor Theories. Scalar-Tensor Theories STT transformation to Einstein frame action Einstein in frame ( ) 2 dφ = 3 dφ 4 ( d ln(f (Φ)) dφ ) 2 + Z(Φ) 2F (Φ) 1 S = 16πG d 4 x g [R 2g µν µ φ ν φ 4V (φ)] + S m [Ψ m ; A 2 (φ)g µν ] relations between the Jordan frame functions F (Φ) and U(Φ) and the Einstein frame functions A(φ) and V (φ) A(φ) = F 1/2 (Φ), 2V (φ) = U(Φ)F 2 (Φ) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
25 Neutron Stars in Scalar-Tensor Theories. Scalar-Tensor Theories STT equations in the Einstein frame R µν 1 2 g µνr = 2 µ φ ν φ g µν g αβ α φ β φ 2V (φ)g µν + 8πG T µν µ d ln(a(φ)) µ φ = 4πG T µ dv (φ) µ + dφ dφ energy momentum tensor: Jordan frame T µν = ( ε + p)ũ µ ũ ν + p g µν energy momentum tensor: Einstein frame T µν = (ε + p)u µ u ν + pg µν A 2 Tµν ε = A 4 (φ) ε, p = A 4 (φ) p, u µ = A 1 (φ)ũ µ Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
26 Neutron Stars in Scalar-Tensor Theories. Scalar-Tensor Theories STT Brans Dicke Theory S = 1 d 4 x [ g 16π ϕr ω(ϕ) ϕ ] gµν ( µ ϕ) ( ν ϕ) U(ϕ) + S M [Ψ, g µν ] relation between Jordan-frame and Einstein-frame quantites ϕ = A 2 (φ), 3 + 2ω(ϕ) = α(φ) 2 α(φ) d(ln A(φ))/dφ α(φ) = α 0 =constant, i.e., ω(ϕ) =constant observational bound: ω > (Cassini-Huygens) limit: ω GR Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
27 Neutron Stars in Scalar-Tensor Theories. Observational Bounds STT Freire et al observational constraints on STT parameters ln A(φ) = ln A(φ 0 ) +α 0 (φ φ 0 ) β 0(φ φ 0 ) 2 Cassini LLR B SEP J B LLR J J m φ = Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
28 Neutron Stars in Scalar-Tensor Theories. Observational Bounds STT Antoniadis et al observational constraints on STT parameters α 0 = β 0 4 top to bottom steps 0.1 m φ = 0 β Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
29 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in STT Theories STT constraints on STT parameters: negligible effect on neutron stars? non-perturbative effects in strong fields: spontaneous scalarization! Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
30 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in STT Theories STT Doneva et al z/r e ln A(φ) = α 0 φ, α 0 < E E E E E E E E E+00 z/r e E E E E E E E E E x/r e static x/r e Kepler limit scalar field φ, neutron star surface (black dashed) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
31 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in STT Theories STT Esposito-Farese (lecture) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
32 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars: Spontaneous Scalarization for example Altaha Motahar et al M (M O ) mass radius relation BHZBM H4 GNH3 GR A 1, β 1 A 1, β 2 A 1 (φ) = e 1 2 βφ2 A 2, β 1 A 2, β 2 1 A 2 (φ) = cosh( βφ) 2.5 β 1 = 4.8 M (M O ) WCS1 WCS2 polytrope β 2 = 4.5 Damour, Esposito-Farese M (M O ) SLy WSPHS1 APR4 WSPHS2 WSPHS3 A 1 (φ) = e 1 2 βφ2 A 3 (φ) = cos( βφ) Jutta2.5 Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
33 Neutron Stars in Scalar-Tensor Theories. Neutron Stars: Spontaneous Scalarization M (M O ) STT BHZBM GR A 1, β 1 A 1, β 2 A 2, β 1 A 2, β H4 GNH3 2.5 M (M O ) WCS1 WCS2 polytrope 2.5 M (M O ) 2 WSPHS1 WSPHS2 1.5 SLy APR4 WSPHS3 2.5 M (M O ) ALF2 ALF4 BS R s (Km) R s (Km) R s (Km) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
34 Neutron Stars in Scalar-Tensor Theories. Neutron Stars: Spontaneous Scalarization ω A H4 BHZBM STT GR A 1, β 1 A 1, β 2 A 2, β 1 A 2, β GNH ω A 0 WCS1 polytrope ω A WCS2 scalar charge ω A φ(r) = ω A r SLy WSPHS1 APR4 WSPHS2 WSPHS ω A 0 ALF2 ALF4 BS M (M O ) M (M O ) M (M O ) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
35 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars: Spontaneous Scalarization for example Altaha Motahar et al β cr fit f(x) polytrope SLy APR4 BHZBM GNH3 H4 WCS1 WCS2 ALF2 ALF4 WSPHS3 WSPHS1 WSPHS2 f(x) = c 0 +c 1 (M/R s ) -1 +c 4 (M/R s ) -4 ω A M/R s onset of scalarization β crit vs compactness M/R fit function A=e βϕ2 /2 β=-4.8 polytrope SLy APR4 BHZBM WCS1 WCS2 GNH3 H4 WSPHS3 ALF2 ALF4 WSPHS1 WSPHS2 BS M/R s scalarized neutron stars scalar charge ω A vs compactness M/R Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
36 Neutron Stars in Scalar-Tensor Theories. Neutron Stars: Spontaneous Scalarization I (10 45 g cm 2 ) 4.5 H BHZBM STT GNH3 GR A 1, β 1 A 1, β 2 A 2, β 1 A 2, β 2 I (10 45 g cm 2 ) 4.5 WCS1 3 WCS2 polytrope 1.5 I (10 45 g cm 2 ) 4.5 WSPHS SLy WSPHS2 APR4 WSPHS3 I (10 45 g cm 2 ) ALF2 ALF4 BS M (M O ) M (M O ) M (M O ) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
37 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars: Spontaneous Scalarization Doneva et al M/M < ln A(φ) = 1 2 β 0φ 2, β 0 > = 0 = -4.2 = -4.5 = R e [km] mass radius M/M < = 0 = -4.2 = -4.5 = x x x x10 15 ~ 2 c / c [ g / cm 3 ] mass energy density spontaneous scalarization: static and Kepler limit Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
38 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars: Spontaneous Scalarization Doneva et al ln A(φ) = 1 2 β 0φ 2, β 0 > c = 0 = -4.2 = -4.5 = x x10 15 ~ 2 / c [ g / cm 3 ] central value of the scalar field vs central energy density static sequences (solid lines) Kepler limit sequences (dotted lines) c Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
39 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars: Spontaneous Scalarization Staykov et al ln A(φ) = 1 2 β 0φ I/(MR 2 ) STT, j = 0.2 GR, j = 0.2 STT, j = 0.4 GR, j = 0.4 STT, j = 0.6 GR, j = 0.6 GR fit, slow rot. 1 - I GR /I fitgr 1 - I STT /I fitstt E-3 1E E-3 1E M/R scaled moment of inertia vs compactness Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
40 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in massive STT Theories STT Alsing et al massive variant of the Brans-Dicke theory bounds on Brans-Dicke coupling parameter ω BD and scalar mass m s Cassini measurements of the Shapiro time delay ω BD > for scalar masses m s < ev Compton wavelengths λ s = h/(m sc) > km Lunar Laser Ranging (LLR) experiments ω BD > 1000 for m s < ev white dwarf-neutron star binary PSR J ω BD > 1250 for m s < ev Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
41 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in massive STT Theories STT Alsing et al Lower bound on (ω BD +3/2) Cassini J J LLR m s (ev) bounds on Brans-Dicke coupling parameter ω BD and scalar mass m s vertical lines: 1 AU (solid), orbital radii (dashed) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
42 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in massive STT Theories STT Alsing et al Lower bound on (ω BD +3/2) Cassini J J LLR m s (ev) bounds on Brans-Dicke coupling parameter ω BD and scalar mass m s consequences: scalar field mass m φ : finite range of the scalar field of order Compton wavelength λ φ no/less stringent constraints for observations involving distances > λ φ Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
43 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in massive STT Theories STT Doneva et al Brans-Dicke theory: A(φ) = e α0φ Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
44 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in massive STT Theories STT Doneva et al slow rotation Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
45 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars in massive STT Theories Ramazoglu et al spontaneous scalarization bounds on scalar mass m φ : bound on the λ φ (m φ ): binary system (with smallest) orbital separation 10 9 m = m φ ev characteristic length scale of star smaller than λ φ m φ 10 9 ev bounds on β white dwarfs: no scalarization 10 3 < β < 3 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
46 Neutron Stars in Scalar-Tensor Theories. Neutron Stars in massive STT Theories STT Ramazoglu et al spontaneous scalarization upper row: m ϕ = ev middle row: m ϕ = lower row: m ϕ = ev left column: β = 4.5 middle column: β = 6 right column: β = 10 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
47 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars in massive STT Theories Doneva et al , static, scalarization: A(φ) = e 1 2 βφ2 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
48 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars in massive STT Theories Doneva et al , slow rotation, scalarization: A(φ) = e 1 2 βφ2 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
49 Neutron Stars in Scalar-Tensor Theories STT. Neutron Stars in massive STT Theories Doneva et al , rapid rotation, scalarization: A(φ) = e 1 2 βφ2 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
50 . Outline Neutron Stars in Scalar-Tensor Theories Horndeski. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
51 . Horndeski gravity Neutron Stars in Scalar-Tensor Theories Horndeski most general scalar-tensor theory with second-order field equations and one scalar field S = d 4 x { g K(ϕ, X) G 3 (ϕ, X) ϕ + G 4 (ϕ, X)R + G 4,X (ϕ, X) [ ( ϕ) 2 ( µ ν ϕ)( µ ν ϕ) ] + G 5 (ϕ, X)G µν µ ν ϕ G 5,X(ϕ, X) [ ( ϕ) 3 3 ϕ( µ ν ϕ)( µ ν ϕ) 6 + 2( µ ν ϕ)( µ σ ϕ)( ν σ ϕ) ]} K and G i s (i = ): functions of the scalar field ϕ and of its kinetic term X = 1/2 µ ϕ µ ϕ G i,x : derivatives of G i with respect to X Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
52 Neutron Stars in Scalar-Tensor Theories Horndeski. Horndeski gravity Charmousis et al , cosmological considerations subsector: Fab Four ) ( S = d4 x g LG [gµν, ϕ] + LM [gµν, Ψ] LG [gµν, ϕ] = Ljohn + Lpaul + Lgeorge + Lringo Jutta Kunz (Universita t Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
53 . Horndeski gravity Neutron Stars in Scalar-Tensor Theories Horndeski Charmousis et al , cosmological considerations subsector: Fab Four S = d 4 x ( ) g L G [g µν, ϕ] + L M [g µν, Ψ] L G [g µν, ϕ] = L george + L ringo + L john + L paul special cases of Horndeski gravity general relativity ( George ) Einstein-dilaton-Gauss-Bonnet gravity ( Ringo ) theories with a nonminimal coupling with the Einstein tensor ( John ) theories involving the double-dual of the Riemann tensor ( Paul ) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
54 µ µ µ µ Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27. Horndeski gravity Neutron Stars in Scalar-Tensor Theories Horndeski Charmousis et al , Fab Four Gauss-Bonnet term L george = V george (ϕ)r L ringo = V ringo (ϕ)r GB L john = V john (ϕ)g µν µ ϕ ν ϕ L paul = V paul (ϕ)p µναβ µ ϕ α ϕ ν β ϕ R GB R αβµν R αβµν 4R µν R µν + R 2 potentials V george (ϕ), V ringo (ϕ), V john (ϕ), and V paul (ϕ) double-dual of the Riemann tensor P µν αβ 1 4 δµνγδ σλαβ Rσλ γδ
55 . Horndeski gravity Neutron Stars in Scalar-Tensor Theories Horndeski Maselli et al John S G = = d 4 x g(l george + L john ) d 4 x [ g κr + 1 ] 2 ηgµν µ ϕ ν ϕ Paul L = L george + L paul = R 1 3 αp µναβ µ ϕ α ϕ ν β ϕ Paul term does not allow for physically well-behaved compact object solutions Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
56 . Horndeski gravity Neutron Stars in Scalar-Tensor Theories Horndeski Maselli et al John mass radius: scalar charge q, dependence on q 2 η (constraints) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
57 . Horndeski gravity Neutron Stars in Scalar-Tensor Theories Horndeski Maselli et al John moment of inertia mass: slow rotation Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
58 . Outline Neutron Stars in Scalar-Tensor Theories f(r). 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
59 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) Theories Motivation: Dark Energy action in f(r) theories of gravity S = 1 d 4 x gf(r) + S matter (g µν, χ) 16πG free of tachyonic instabilities and ghosts d 2 f/dr 2 0, df/dr > 0 mathematically equivalent to STT S = 1 d 4 x g [ΦR U(Φ)] + S matter (g µν, χ) 16πG Φ = df(r) dr, U(Φ) = R df dr f(r) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
60 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) Theories Yazadjiev et al , , Einstein frame with metric g µν conformal transformation action S = 1 16πG g µν = Φg µν d 4 x g [R 2g µν µ φ ν φ V (φ)] + S matter (e 2 3 φ g µν, χ) new scalar field φ Einstein frame potential V (φ) φ = 3 2 ln Φ V (φ) = A 4 (φ)u(φ(φ)) A 2 (φ) = Φ 1 (φ) = e 2 3 φ Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
61 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) = R + ar 2 Theory Yazadjiev et al , , R-squared gravity inequalities f(r) = R + ar 2 a 0, 1 + 2aR 0 gravitational scalar field and potential Φ = df(r) dr, U(Φ) = R df dr f(r) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
62 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) = R + ar 2 Theory Yazadjiev et al , , M/M < EOS SLy4 GR a=0.3 a=1 a=10 a=10 2 a= R S [km] M/M < EOS APR4 GR a=0.3 a=1 a=10 a=10 2 a= R S [km] mass radius relation SLy4 APR4 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
63 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) = R + ar 2 Theory Yazadjiev et al , , non-perturbative static results:...the differences between the R-squared gravity and general relativity are comparable with the uncertainties in the nuclear matter equations of state. That is why the current observations of the neutron star masses and radii alone cannot put constraints on the value of the parameters a, unless the equation of state is better constrained in the future. Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
64 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) = R + ar 2 Theory Yazadjiev et al , , I APR4 GR a=0.3 a=1 a=10 a=10 2 a=10 4 SLy4 SQSB M/M < M/M < M/M < slow rotation: moment of inertia mass relation APR4 SLy4 SQSB60 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
65 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) = R + ar 2 Theory Yazadjiev et al , , non-perturbative slowly rotating results:...the neutron star moment of inertia can be up to 30% larger compared to the corresponding general relativistic models. This is much higher than the change in the maximum mass induced by R-squared gravity and is beyond the EOS uncertainty. In this way the future observations of the moment of inertia of compact stars could allow us to distinguish between general relativity and f(r) gravity, and more generally to test the strong field regime of gravity. Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
66 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) = R + ar 2 Theory Yazadjiev et al , , M/M static solutions at the Kepler frequency EOS APR4 GR a = 1 a = 10 a = 10 2 a = 10 4 static solutions at the Kepler frequency EOS SLy R e Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27 R e
67 Neutron Stars in Scalar-Tensor Theories f(r). Neutron Stars in f(r) = R + ar 2 Theory Yazadjiev et al , , I EOS APR4 GR a = 1 a = 10 a = 10 2 a = 10 4 at the Kepler frequency static solutions M/M EOS SLy4 at the Kepler frequency static solutions M/M Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
68 . Outline Neutron Stars in Quadratic Gravity. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
69 Neutron Stars in Quadratic Gravity. Quadratic Gravity Curvature invariants R 2, Rµν 2, Rµνρσ 2, RR Rµν 2 R µν R µν Kretschmann scalar Rµνρσ 2 R µνρσ R µνρσ Pontryagin/Chern-Simons scalar RR 1 2 R µνρσϵ νµλκ R ρσ λκ Levi-Civita tensor ϵ µνρσ Gauss-Bonnet scalar R 2 GB R 2 4R 2 µν + R 2 µνρσ Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
70 Neutron Stars in Quadratic Gravity. Quadratic Gravity most generic class of four-dimensional theories: all quadratic algebraic curvature invariants coupled to a single scalar field S = 1 gd x[ 4 R 2 µ ϕ µ ϕ V (ϕ) 16π ] + f 1 (ϕ)r 2 + f 2 (ϕ)r µν R µν + f 3 (ϕ)r µνρσ R µνρσ + f 4 (ϕ) RR + S mat [Ψ, γ(ϕ)g µν ], coupling functions f i, potential V generic properties weak equivalence principle higher-order field equations appearance of ghosts Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
71 . Outline Neutron Stars in Quadratic Gravity EGBd Theory. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
72 Neutron Stars in Quadratic Gravity EGBd Theory. Einstein-Gauss-Bonnet-Dilaton Theory String Theory unification of all fundamental interactions dimensional reduction to 4 spacetime dimensions: low energy effective theories additional fields dilaton axion Maxwell fields Yang-Mills fields... higher order curvature corrections Gauss-Bonnet term Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
73 Neutron Stars in Quadratic Gravity EGBd Theory. Einstein-Gauss-Bonnet-Dilaton Theory Action S = 1 16π d 4 x [ g R 1 2 ( µϕ) 2 + α ] 4 e γϕ RGB 2 Gauss-Bonnet term: quadratic in the curvature R 2 GB = R µνρσ R µνρσ 4R µν R µν + R 2 α Gauss-Bonnet coupling constant γ dilaton coupling constant (γ = 1) In 4 spacetime dimensions the coupling to the dilaton is needed. The resulting set of equations of motion are of second order. Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
74 Neutron Stars in Quadratic Gravity EGBd Theory. Einstein-Gauss-Bonnet-Dilaton Theory modified Einstein equations G µν = 1 2 T eff µν where Tµν eff = T µν (ϕ) α 2 e γϕ T µν (GBd) T (ϕ) µν = µ ϕ ν ϕ 1 2 g µν λ ϕ λ ϕ dilaton equation T (GBd) µν = H µν + 4 ( γ 2 ρ ϕ σ ϕ γ ρ σ ϕ ) P µρνσ 2 ϕ = αγ 4 e γϕ R 2 GB Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
75 Neutron Stars in Quadratic Gravity EGBd Theory. Einstein-Gauss-Bonnet-Dilaton Theory consequences scalar hair : dilaton hair negative energy density bounds on α (γ = 1) observational Shapiro time delay α cm BH low-mass X-ray binaries α cm theoretical/observational lower bound on BH mass α M 2 Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
76 Neutron Stars in Quadratic Gravity EGBd Theory. Einstein-Gauss-Bonnet-Dilaton Theory constraints from black holes 10 α L 10 α (10 5 cm) γα= cm BH 1 BH 2 BH 3 GRO J α (10 5 cm) α L γα= cm BH 1 BH 2 BH 3 GRO J regular dilatonic black holes, γ= M (M O ) 2 regular dilatonic black holes, γ= M (M O ) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
77 Neutron Stars in Quadratic Gravity EGBd Theory. Einstein-Gauss-Bonnet-Dilaton Theory different names: EdGB EGBd degb... different notations, different units α in cm 2 α in M 2 α dimensionless... Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
78 Neutron Stars in Quadratic Gravity EGBd Theory. Compact Stars in EGBd Theory S = 1 16π d 4 x g [R 12 ( µϕ) 2 + α4 ] e γϕ R 2GB + L matt α Gauss=Bonnet coupling constant dilaton coupling constant (γ = 1, β = 2) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
79 Neutron Stars in Quadratic Gravity EGBd Theory. Compact Stars in EGBd Theory Pani et al static neutron stars with APR EoS: dependence on α and β branches end expansion around origin: square roots reality condition: condition on αβ, maximum central density Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
80 Neutron Stars in Quadratic Gravity EGBd Theory. Compact Stars in EGBd Theory Pani et al perturbative result: moment of inertia I = J/Ω for slow rotation Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
81 Neutron Stars in Quadratic Gravity EGBd Theory. Rapidly Rotating Neutron Stars in EGBd Theory Kleihaus et al (α = α L) EOS FPS EOS DI-II α=0.0 α=1.0 α=2.0 EOS: FPS α=0.0 α=1.0 α=2.0 EOS: DI-II M[M ] 1.6 M[M ] static static R e [km] R e [km] domain of existence: static, secular instability, Kepler limit Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
82 Neutron Stars in Quadratic Gravity EGBd Theory. Rapidly Rotating Neutron Stars in EGBd Theory Kleihaus et al (α = α L) EOS DI-II EOS DI-II 2.3 EOS: DI-II 4 EOS: DI-II α=1.0 M[M ] α=0.0 α=1.0 α=2.0 Ω=0.020 Ω=0.030 Ω= ε c /c 2 [10 15 g/cm 3 ] I/10 45 [g cm 2 ] 3 α= Ω=0.020 Ω=0.030 Ω= M[M ] mass energy density moment of inertia mass Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
83 Neutron Stars in Quadratic Gravity EGBd Theory. Rapidly Rotating Neutron Stars in EGBd Theory Kleihaus et al (α = α L) EOS DI-II EOS DI-II 0 35 EOS: DI-II α= α=2.0 α=1.0 q/r Ω=0.020 α= Ω=0.030 Ω=0.038 EOS: DI-II M[M ] Q[M km 2 ] Ω=0.020 Ω=0.030 Ω= M[M ] dilaton charge mass quadrupole moment mass Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
84 Neutron Stars in Quadratic Gravity EGBd Theory. Rapidly Rotating Neutron Stars in EGBd Theory Kleihaus et al (α = α L) EOS DI-II EOS DI-II EOS: DI-II α=1.0 (d) M=2.08 M, R e =12.3 km M=1.40 M, R e =19.8 km isometric embedding energy density (10 15 g/cm 3 ) Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
85 . EGBd Wormholes Neutron Stars in Quadratic Gravity EGBd Theory Kanti et al , acceleration of a traveler at the throat? g : acceleration of gravity at the surface of the earth acceleration on the order of g : throat radius on the order of (10 100) light-years Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
86 . Outline Neutron Stars in Quadratic Gravity dcs Theory. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
87 Neutron Stars in Quadratic Gravity dcs Theory. Neutron Stars in Chern-Simons Gravity action two cases dynamical: S = 1 gd 4 x [R 2 µ ϕ µ ϕ V (ϕ) + α CS ϕ RR] 16π scalar true dynamical degree of freedom dcs gravity nondynamical: scalar kinetic term absent a spherically symmetric solution of GR is also a solution of dcs gravity corrections in the presence of a parity-odd source such as rotation bound: Gravity Probe B αcs < O(10 13 )cm Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
88 Neutron Stars in Quadratic Gravity dcs Theory. Neutron Stars in Chern-Simons Gravity Yagi et al st order α CS 2nd order J Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
89 Neutron Stars in Quadratic Gravity dcs Theory. Neutron Stars in Chern-Simons Gravity Yagi et al CS correction to quadrupole moment CS correction to angular momentum Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
90 . Outline Outlook. 1 Motivation. 2 Neutron Stars in General Relativity. 3 Neutron Stars in Scalar-Tensor Theories STT Horndeski f(r). 4 Neutron Stars in Quadratic Gravity EGBd Theory dcs Theory. 5 Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
91 . Outlook Outlook Jutta Kunz (Universität Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
92 Outlook. Thanks THANKS! Jutta Kunz (Universita t Oldenburg) Neutron Stars in Alternative Theories of Gravity NewCompStar School Sofia / 27
2 Post-Keplerian Timing Parameters for General Relativity
1 Introduction General Relativity has been one of the pilars of modern physics for over 100 years now. Testing the theory and its consequences is therefore very important to solidifying our understand
Black-Hole Solutions with Scalar Hair in Einstein-Scalar-Gauss-Bonnet Theories
Black-Hole Solutions with Scalar Hair in Einstein-Scalar-Gauss-Bonnet Theories Athanasios Bakopoulos Physics Department University of Ioannina In collaboration with: George Antoniou and Panagiota Kanti
Gravity and scalar fields. Thomas P. Sotiriou SISSA - International School for Advanced Studies, Trieste (...soon at the University of Nottingham)
Gravity and scalar fields Thomas P. Sotiriou SISSA - International School for Advanced Studies, Trieste (...soon at the University of Nottingham) µm 1AU 15Mpc Quantum Gravity General Relativity plus unknown
Black-hole binaries in Einstein-dilaton Gauss Bonnet gravity
Black-hole binaries in Einstein-dilaton Gauss Bonnet gravity Helvi Witek Theoretical Particle Physics and Cosmology Department of Physics, King s College London work in progress with L. Gualtieri, P. Pani,
Universal Relations for the Moment of Inertia in Relativistic Stars
Universal Relations for the Moment of Inertia in Relativistic Stars Cosima Breu Goethe Universität Frankfurt am Main Astro Coffee Motivation Crab-nebula (de.wikipedia.org/wiki/krebsnebel) neutron stars
D. f(r) gravity. φ = 1 + f R (R). (48)
5 D. f(r) gravity f(r) gravity is the first modified gravity model proposed as an alternative explanation for the accelerated expansion of the Universe [9]. We write the gravitational action as S = d 4
arxiv: v1 [gr-qc] 19 Jan 2015
![arxiv: v1 [gr-qc] 19 Jan 2015](/thumbs/78/77445191.jpg "arxiv: v1 [gr-qc] 19 Jan 2015")
Rapidly rotating neutron stars in R-squared gravity Stoytcho S. Yazadjiev, 1, 2, Daniela D. Doneva, 2,, and Kostas D. Kokkotas 2, 1 Department of Theoretical Physics, Faculty of Physics, Sofia University,
Neutron-star mergers in scalartensor theories of gravity
Neutron-star mergers in scalartensor theories of gravity Enrico Barausse (Institut d'astrophysique de Paris, France) in collaboration with Carlos Palenzuela (CITA, Canada), Luis Lehner (Perimeter Institute,
A brief introduction to modified theories of gravity
(Vinc)Enzo Vitagliano CENTRA, Lisboa May, 14th 2015 IV Amazonian Workshop on Black Holes and Analogue Models of Gravity Belém do Pará The General Theory of Relativity dynamics of the Universe behavior
From Gravitation Theories to a Theory of Gravitation
From Gravitation Theories to a Theory of Gravitation Thomas P. Sotiriou SISSA/ISAS, Trieste, Italy based on 0707.2748 [gr-qc] in collaboration with V. Faraoni and S. Liberati Sep 27th 2007 A theory of
Black-hole binary inspiral and merger in scalar-tensor theory of gravity
Black-hole binary inspiral and merger in scalar-tensor theory of gravity U. Sperhake DAMTP, University of Cambridge General Relativity Seminar, DAMTP, University of Cambridge 24 th January 2014 U. Sperhake
Strong field tests of Gravity using Gravitational Wave observations
Strong field tests of Gravity using Gravitational Wave observations K. G. Arun Chennai Mathematical Institute Astronomy, Cosmology & Fundamental Physics with GWs, 04 March, 2015 indig K G Arun (CMI) Strong
Constraints on the deviations from general relativity
14/10/2010 Minneapolis Constraints on the deviations from general relativity From local to cosmological scales Jean-Philippe UZAN GR in a nutshell Underlying hypothesis Equivalence principle Universality
Trapped ghost wormholes and regular black holes. The stability problem
Trapped ghost wormholes and regular black holes. The stability problem Kirill Bronnikov in collab. with Sergei Bolokhov, Arislan Makhmudov, Milena Skvortsova (VNIIMS, Moscow; RUDN University, Moscow; MEPhI,
Neutron Stars as Laboratories for Gravity Physics
Neutron Stars as Laboratories for Gravity Physics Cemsinan Deliduman Department of Physics, Mimar Sinan University, Turkey S. Arapoglu, C.D., K.Y. Ekşi, JCAP 1107 (2011) 020 [arxiv:1003.3179]. C.D., K.Y.
Accelerating Cosmologies and Black Holes in the Dilatonic Einstein-Gauss-Bonnet (EGB) Theory
Accelerating Cosmologies and Black Holes in the Dilatonic Einstein-Gauss-Bonnet (EGB) Theory Zong-Kuan Guo Fakultät für Physik, Universität Bielefeld Zong-Kuan Guo (Universität Bielefeld) Dilatonic Einstein-Gauss-Bonnet
arxiv:gr-qc/ v1 15 Mar 1999
CPT-99/P.3802 gr-qc/9903058 COMPARING SOLAR-SYSTEM, BINARY-PULSAR, AND GRAVITATIONAL-WAVE TESTS OF GRAVITY a arxiv:gr-qc/9903058v1 15 Mar 1999 Gilles ESPOSITO-FARESE Centre de Physique Théorique, CNRS
An all-scale exploration of alternative theories of gravity. Thomas P. Sotiriou SISSA - International School for Advanced Studies, Trieste
An all-scale exploration of alternative theories of gravity Thomas P. Sotiriou SISSA - International School for Advanced Studies, Trieste General Outline Beyond GR: motivation and pitfalls Alternative
The dilaton and modified gravity
The dilaton and modified gravity Carsten van de Bruck University of Sheffield Work in collaboration with P. Brax, A. Davis and D. Shaw arxiv:1005.3735 Scalar Fields and Modified Gravity Scalar fields are
Synergizing Screening Mechanisms on Different Scales
Synergizing Screening Mechanisms on Different Scales Jeremy Sakstein University of Pennsylvania Probing the dark sector and general relativity at all scales CERN 17 th August 2017 Or. What should astrophysical
Gravity Tests with Radio Pulsars
Gravity Tests with Radio Pulsars Norbert Wex Paris, June 21 st, 2010 Regimes of Gravity Tests (1) Quasi-stationary weak-field regime Solar system experiments (2) Quasi-stationary strong-field regime (3)
Gravity with the SKA
Gravity with the SKA Strong-field tests of gravity using Pulsars and Black Holes Michael Kramer Jodrell Bank Observatory University of Manchester With Don Backer, Jim Cordes, Simon Johnston, Joe Lazio
Non-perturbative and self-consistent models of neutron stars in R-squared gravity
Prepared for submission to JCAP arxiv:1402.4469v2 [gr-qc] 2 Jun 2014 Non-perturbative and self-consistent models of neutron stars in R-squared gravity Stoytcho S. Yazadjiev, a,b Daniela D. Doneva, a Kostas
arxiv: v1 [gr-qc] 1 Jan 2019
![arxiv: v1 [gr-qc] 1 Jan 2019](/thumbs/93/112621849.jpg "arxiv: v1 [gr-qc] 1 Jan 2019")
Jordan frame beyond scalar-tensor theories arxiv:90.0094v gr-qc Jan 209 Fethi M. Ramazanoğlu Department of Physics, Koç University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey (Dated: January 3,
Lecture: General Theory of Relativity
Chapter 8 Lecture: General Theory of Relativity We shall now employ the central ideas introduced in the previous two chapters: The metric and curvature of spacetime The principle of equivalence The principle
Experimental Tests and Alternative Theories of Gravity
Experimental Tests and Alternative Theories of Gravity Gonzalo J. Olmo Alba gonzalo.olmo@uv.es University of Valencia (Spain) & UW-Milwaukee Experimental Tests and Alternative Theories of Gravity p. 1/2
Dilaton gravity at the brane with general matter-dilaton coupling
Dilaton gravity at the brane with general matter-dilaton coupling University of Würzburg, Institute for Theoretical Physics and Astrophysics Bielefeld, 6. Kosmologietag May 5th, 2011 Outline introduction
Classification theorem for the static and asymptotically flat Einstein-Maxwell-dilaton spacetimes possessing a photon sphere
Classification theorem for the static and asymptotically flat Einstein-Maxwell-dilaton spacetimes possessing a photon sphere Boian Lazov and Stoytcho Yazadjiev Varna, 2017 Outline 1 Motivation 2 Preliminaries
Challenges in Cosmology and why (may be) Modified Gravity
Challenges in Cosmology and why (may be) Modified Gravity David F. Mota Institute for Research in Fundamental Sciences IPM-Teheran 2016 Two Pillars in Cosmology Understanding the Universe and its laws
2.5.1 Static tides Tidal dissipation Dynamical tides Bibliographical notes Exercises 118
ii Contents Preface xiii 1 Foundations of Newtonian gravity 1 1.1 Newtonian gravity 2 1.2 Equations of Newtonian gravity 3 1.3 Newtonian field equation 7 1.4 Equations of hydrodynamics 9 1.4.1 Motion of
Neutron and quark stars in f (R) gravity
9th A. Friedmann International Seminar and 3rd Casimir Symposium 05 International Journal of Modern Physics: Conference Series Vol. 4 (06) 66030 (9 pages) c The Author(s) DOI: 0.4/S00945660307 Neutron
Galileons. Axions and the Low Energy Frontier. Philippe Brax IPhT Saclay
Galileons Axions and the Low Energy Frontier Philippe Brax IPhT Saclay Comment le sait-on? Mesure de distances! Dark Energy: anything which leads to the late time acceleration of the expansion of the Universe!
Black Holes in Higher-Derivative Gravity. Classical and Quantum Black Holes
Black Holes in Higher-Derivative Gravity Classical and Quantum Black Holes LMPT, Tours May 30th, 2016 Work with Hong Lü, Alun Perkins, Kelly Stelle Phys. Rev. Lett. 114 (2015) 17, 171601 Introduction Black
Non-gravitating waves
Non-gravitating waves D C Robinson Mathematics Department King s College London Strand London WC2R 2LS United Kingdom email: david.c.robinson@kcl.ac.uk October 6, 2005 Abstract: It is pointed out that
The Influence of DE on the Expansion Rate of the Universe and its Effects on DM Relic Abundance
The Influence of DE on the Expansion Rate of the Universe and its Effects on DM Relic Abundance Esteban Jimenez Texas A&M University XI International Conference on Interconnections Between Particle Physics
Einstein s Theory of Gravity. December 13, 2017
December 13, 2017 Newtonian Gravity Poisson equation 2 U( x) = 4πGρ( x) U( x) = G ρ( x) x x d 3 x For a spherically symmetric mass distribution of radius R U(r) = 1 r U(r) = 1 r R 0 r 0 r 2 ρ(r )dr for
Tests of cosmological gravity
Tests of cosmological gravity Jeremy Sakstein University of Pennsylvania Astrophysics Seminar UC Irvine 23 rd January 2018 Who am I? Particle-cosmology (baryogenesis, early universe) Modified gravity (dark
Gravitational waves, solitons, and causality in modified gravity
Gravitational waves, solitons, and causality in modified gravity Arthur Suvorov University of Melbourne December 14, 2017 1 of 14 General ideas of causality Causality as a hand wave Two events are causally
arxiv: v1 [gr-qc] 18 Jan 2019
![arxiv: v1 [gr-qc] 18 Jan 2019](/thumbs/88/114652503.jpg "arxiv: v1 [gr-qc] 18 Jan 2019")
A new type of dark compact objects in massive tensor-multi-scalar theories of gravity Stoytcho S. Yazadjiev 1, 2, 3, and Daniela D. Doneva1, 4, 1 Theoretical Astrophysics, Eberhard Karls University of
Einstein s Equations. July 1, 2008
July 1, 2008 Newtonian Gravity I Poisson equation 2 U( x) = 4πGρ( x) U( x) = G d 3 x ρ( x) x x For a spherically symmetric mass distribution of radius R U(r) = 1 r U(r) = 1 r R 0 r 0 r 2 ρ(r )dr for r
Gravitational radiation
Lecture 28: Gravitational radiation Gravitational radiation Reading: Ohanian and Ruffini, Gravitation and Spacetime, 2nd ed., Ch. 5. Gravitational equations in empty space The linearized field equations
Geometry of SpaceTime Einstein Theory. of Gravity II. Max Camenzind CB Oct-2010-D7
Geometry of SpaceTime Einstein Theory of Gravity II Max Camenzind CB Oct-2010-D7 Textbooks on General Relativity Geometry of SpaceTime II Connection and curvature on manifolds. Sectional Curvature. Geodetic
Dynamics of star clusters containing stellar mass black holes: 1. Introduction to Gravitational Waves
Dynamics of star clusters containing stellar mass black holes: 1. Introduction to Gravitational Waves July 25, 2017 Bonn Seoul National University Outline What are the gravitational waves? Generation of
Chern-Simons Gravity:
Chern-Simons Gravity: its effects on bodies orbiting the Earth Adrienne Erickcek (Caltech) Tristan Smith (Caltech) Robert Caldwell (Dartmouth) Marc Kamionkowski (Caltech) arxiv: 0708.0001, to appear in
Beyond Einstein: gravitational waves from extended gravities
Beyond Einstein: gravitational waves from extended gravities Salvatore Capozziello Università di Napoli Federico II and INFN sez. di Napoli in collaboration with Mariafelicia De Laurentis Institute for
Colliding scalar pulses in the Einstein-Gauss-Bonnet gravity
Colliding scalar pulses in the Einstein-Gauss-Bonnet gravity Hisaaki Shinkai 1, and Takashi Torii 2, 1 Department of Information Systems, Osaka Institute of Technology, Hirakata City, Osaka 573-0196, Japan
Probing Relativistic Gravity with the Double Pulsar
Probing Relativistic Gravity with the Double Pulsar Marta Burgay INAF Osservatorio Astronomico di Cagliari The spin period of the original millisecond pulsar PSR B1937+21: P = 0.0015578064924327 ± 0.0000000000000004
A rotating charged black hole solution in f (R) gravity
PRAMANA c Indian Academy of Sciences Vol. 78, No. 5 journal of May 01 physics pp. 697 703 A rotating charged black hole solution in f R) gravity ALEXIS LARRAÑAGA National Astronomical Observatory, National
On Black Hole Structures in Scalar-Tensor Theories of Gravity
On Black Hole Structures in Scalar-Tensor Theories of Gravity III Amazonian Symposium on Physics, Belém, 2015 Black holes in General Relativity The types There are essentially four kind of black hole solutions
, G RAVITATIONAL-WAVE. Kent Yagi. with N. Yunes. Montana State University. YKIS2013, Kyoto
UNIVERSAL I-LOVE OVE-Q Q RELATIONSR IN Q R NEUTRON STARS AND THEIR APPLICATIONS TO ASTROPHYSICS STROPHYSICS,, GRAVITATIONAL G RAVITATIONAL-WAVE AVE, G AND FUNDAMENTAL PHYSICS Kent Yagi with N. Yunes Montana
Status of Hořava Gravity
Status of Institut d Astrophysique de Paris based on DV & T. P. Sotiriou, PRD 85, 064003 (2012) [arxiv:1112.3385 [hep-th]] DV & T. P. Sotiriou, JPCS 453, 012022 (2013) [arxiv:1212.4402 [hep-th]] DV, arxiv:1502.06607
arxiv: v1 [gr-qc] 6 Dec 2018
![arxiv: v1 [gr-qc] 6 Dec 2018](/thumbs/92/107936813.jpg "arxiv: v1 [gr-qc] 6 Dec 2018")
Innermost stable circular orbits of neutron stars in dilatonic-einstein-gauss-bonnet theory Guillermo A. González 1, Burkhard Kleihaus, Jutta Kunz and Sindy Mojica 1 1 Grupo de Investigación en Relatividad
Covariant Equations of Motion of Extended Bodies with Mass and Spin Multipoles
Covariant Equations of Motion of Extended Bodies with Mass and Spin Multipoles Sergei Kopeikin University of Missouri-Columbia 1 Content of lecture: Motivations Statement of the problem Notable issues
HOMEWORK 10. Applications: special relativity, Newtonian limit, gravitational waves, gravitational lensing, cosmology, 1 black holes
General Relativity 8.96 (Petters, spring 003) HOMEWORK 10. Applications: special relativity, Newtonian limit, gravitational waves, gravitational lensing, cosmology, 1 black holes 1. Special Relativity
Mathematical and Physical Foundations of Extended Gravity (II)
Mathematical and Physical Foundations of Extended Gravity (II) -The Gravitational Waves era- Salvatore Capozziello Università di Napoli Federico II INFN sez. di Napoli SIGRAV Open Fundamental Issues! What
Extended mimetic gravity:
Extended mimetic gravity: Hamiltonian analysis and gradient instabilities Kazufumi Takahashi (JSPS fellow) Rikkyo University Based on KT, H. Motohashi, T. Suyama, and T. Kobayashi Phys. Rev. D 95, 084053
Gravitational radiation from compact binaries in scalar-tensor gravity
Gravitational radiation from compact binaries in scalar-tensor gravity Ryan Lang University of Florida 10th International LISA Symposium May 23, 2014 Testing general relativity General relativity has withstood
Dark Energy and Dark Matter Interaction. f (R) A Worked Example. Wayne Hu Florence, February 2009
Dark Energy and Dark Matter Interaction f (R) A Worked Example Wayne Hu Florence, February 2009 Why Study f(r)? Cosmic acceleration, like the cosmological constant, can either be viewed as arising from
Gauss-Bonnet Gravity with Scalar Field in Four Dimensions
arxiv:0707.0347v3 [gr-qc] 13 Jul 2007 Gauss-Bonnet Gravity with Scalar Field in Four Dimensions Metin Gürses Department of Mathematics, Faculty of Sciences Bilkent University, 06800 Ankara - Turkey March
Numerical black hole mergers beyond general relativity
Numerical black hole mergers beyond general relativity Leo C. Stein (Theoretical astrophysics @ Caltech) 2018 2 23 YKIS2018a Preface Me, Kent Yagi, Nico Yunes Takahiro Tanaka Maria (Masha) Okounkova Many
Applications of Neutron-Star Universal Relations to Gravitational Wave Observations
Applications of Neutron-Star Universal Relations to Gravitational Wave Observations Department of Physics, Montana State University INT, Univ. of Washington, Seattle July 3rd 2014 Universal Relations:
Einstein Double Field Equations
Einstein Double Field Equations Stephen Angus Ewha Woman s University based on arxiv:1804.00964 in collaboration with Kyoungho Cho and Jeong-Hyuck Park (Sogang Univ.) KIAS Workshop on Fields, Strings and
Holographic self-tuning of the cosmological constant
Holographic self-tuning of the cosmological constant Francesco Nitti Laboratoire APC, U. Paris Diderot IX Crete Regional Meeting in String Theory Kolymbari, 10-07-2017 work with Elias Kiritsis and Christos
Introduction to the Vainshtein mechanism
Introduction to the Vainshtein mechanism Eugeny Babichev LPT, Orsay School Paros 23-28 September 2013 based on arxiv:1107.1569 with C.Deffayet OUTLINE Introduction and motivation k-mouflage Galileons Non-linear
Equation of state of dark energy. Phys. Rev. D 91, (2015)
Equation of state of dark energy in f R gravity The University of Tokyo, RESCEU K. Takahashi, J. Yokoyama Phys. Rev. D 91, 084060 (2015) Motivation Many modified theories of gravity have been considered
No hair theorems and compact objects in Horndeski theories
No hair theorems and compact objects in Horndeski theories LPT Orsay, CNRS 9th Aegean Summer School Sifnos 1 Introduction: From scalar-tensor to Horndeski theory and beyond 2 3 4 Fact: GR is a unique theory
Dark Energy to Modified Gravity
Dark Energy to Modified Gravity Philippe Brax IPhT Saclay Workshop Invisibles July 2014 Paris The Big Puzzle Acceleration of the expansion Dark Energy? Modified gravity on large enough scales? The acceleration
Quantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
Solar system tests for linear massive conformal gravity arxiv: v1 [gr-qc] 8 Apr 2016
![Solar system tests for linear massive conformal gravity arxiv: v1 [gr-qc] 8 Apr 2016](/thumbs/72/66412163.jpg "Solar system tests for linear massive conformal gravity arxiv: v1 [gr-qc] 8 Apr 2016")
Solar system tests for linear massive conformal gravity arxiv:1604.02210v1 [gr-qc] 8 Apr 2016 F. F. Faria Centro de Ciências da Natureza, Universidade Estadual do Piauí, 64002-150 Teresina, PI, Brazil
Rotating Black Holes in Higher Dimensions
Rotating Black Holes in Higher Dimensions Jutta Kunz Institute of Physics CvO University Oldenburg Models of Gravity in Higher Dimensions Bremen, 25.-29. 8. 2008 Jutta Kunz (Universität Oldenburg) Rotating
Inflationary cosmology from higher-derivative gravity
Inflationary cosmology from higher-derivative gravity Sergey D. Odintsov ICREA and IEEC/ICE, Barcelona April 2015 REFERENCES R. Myrzakulov, S. Odintsov and L. Sebastiani, Inflationary universe from higher-derivative
Finding Horndeski theories with Einstein gravity limits
Prepared for submission to JCAP Finding Horndeski theories with Einstein gravity limits arxiv:1606.03282v1 [gr-qc] 10 Jun 2016 Ryan McManus, a Lucas Lombriser, a Jorge Peñarrubia a a Institute for Astronomy,
1 Introduction. 1.1 Notations and conventions
The derivation of the coupling constant in the new Self Creation Cosmology Garth A Barber The Vicarage, Woodland Way, Tadworth, Surrey, England KT206NW Tel: +44 01737 832164 e-mail: garth.barber@virgin.net
Is Cosmic Acceleration Telling Us Something About Gravity?
Is Cosmic Acceleration Telling Us Something About Gravity? Mark Trodden Syracuse University [See many other talks at this meeting; particularly talks by Carroll, Dvali, Deffayet,... ] NASA Meeting: From
Parameterizing and constraining scalar corrections to GR
Parameterizing and constraining scalar corrections to GR Leo C. Stein Einstein Fellow Cornell University Texas XXVII 2013 Dec. 12 The takeaway Expect GR needs correction Look to compact binaries for corrections
Compact Stars in the Braneworld
Compact Stars in the Braneworld Mike Georg Bernhardt Zentrum für Astronomie Heidelberg Landessternwarte 28 January 29 Outline Review: Relativistic Stars TOV equations Solutions of the TOV equations Neutron
The Geometric Scalar Gravity Theory
The Geometric Scalar Gravity Theory M. Novello 1 E. Bittencourt 2 J.D. Toniato 1 U. Moschella 3 J.M. Salim 1 E. Goulart 4 1 ICRA/CBPF, Brazil 2 University of Roma, Italy 3 University of Insubria, Italy
Cosmology and Gravitational Bags via Metric-Independent Volume-Form Dynamics
1 Cosmology and Gravitational Bags via Metric-Independent Volume-Form Dynamics XI International Workshop Lie Theory and Its Applications, Varna 2015 Eduardo Guendelman 1, Emil Nissimov 2, Svetlana Pacheva
Anisotropic Interior Solutions in Hořava Gravity and Einstein-Æther Theory
Anisotropic Interior Solutions in and Einstein-Æther Theory CENTRA, Instituto Superior Técnico based on DV and S. Carloni, arxiv:1706.06608 [gr-qc] Gravity and Cosmology 2018 Yukawa Institute for Theoretical
arxiv:gr-qc/ v3 11 Aug 1998
No Scalar Hair Theorem for a Charged Spherical Black Hole arxiv:gr-qc/9803019v3 11 Aug 1998 N.Banerjee and S.Sen Relativity and Cosmology Research Centre, Department of Physics, Jadavpur University, Calcutta-700032,
Lecture 9: RR-sector and D-branes
Lecture 9: RR-sector and D-branes José D. Edelstein University of Santiago de Compostela STRING THEORY Santiago de Compostela, March 6, 2013 José D. Edelstein (USC) Lecture 9: RR-sector and D-branes 6-mar-2013
A Panorama of Modified Gravity. Philippe Brax IPhT Saclay
A Panorama of Modified Gravity Philippe Brax IPhT Saclay The Universe accelerates: why? Maybe a landscape of Universes? Or not? The acceleration of the Universe could also be due to many mundane causes:
Backreaction effects of matter coupled higher derivative gravity
Backreaction effects of matter coupled higher derivative gravity Lata Kh Joshi (Based on arxiv:1409.8019, work done with Ramadevi) Indian Institute of Technology, Bombay DAE-HEP, Dec 09, 2014 Lata Joshi
Einstein Toolkit Workshop. Joshua Faber Apr
Einstein Toolkit Workshop Joshua Faber Apr 05 2012 Outline Space, time, and special relativity The metric tensor and geometry Curvature Geodesics Einstein s equations The Stress-energy tensor 3+1 formalisms
Einstein-Maxwell-Chern-Simons Black Holes
.. Einstein-Maxwell-Chern-Simons Black Holes Jutta Kunz Institute of Physics CvO University Oldenburg 3rd Karl Schwarzschild Meeting Gravity and the Gauge/Gravity Correspondence Frankfurt, July 2017 Jutta
The nonlinear dynamical stability of infrared modifications of gravity
The nonlinear dynamical stability of infrared modifications of gravity Aug 2014 In collaboration with Richard Brito, Vitor Cardoso and Matthew Johnson Why Study Modifications to Gravity? General relativity
Übungen zu RT2 SS (4) Show that (any) contraction of a (p, q) - tensor results in a (p 1, q 1) - tensor.
Übungen zu RT2 SS 2010 (1) Show that the tensor field g µν (x) = η µν is invariant under Poincaré transformations, i.e. x µ x µ = L µ νx ν + c µ, where L µ ν is a constant matrix subject to L µ ρl ν ση
Modified Gravity. Santiago E. Perez Bergliaffa. Department of Theoretical Physics Institute of Physics University of the State of Rio de Janeiro
Modified Gravity Santiago E. Perez Bergliaffa Department of Theoretical Physics Institute of Physics University of the State of Rio de Janeiro BSCG 14 Summary What is modified gravity (MG)? Relevance:
Post-Keplerian effects in binary systems
Post-Keplerian effects in binary systems Laboratoire Univers et Théories Observatoire de Paris / CNRS The problem of binary pulsar timing (Credit: N. Wex) Some classical tests of General Relativity Gravitational
Braneworlds: gravity & cosmology. David Langlois APC & IAP, Paris
Braneworlds: gravity & cosmology David Langlois APC & IAP, Paris Outline Introduction Extra dimensions and gravity Large (flat) extra dimensions Warped extra dimensions Homogeneous brane cosmology Brane
Testing Gravity using Astrophysics
Testing Gravity using Astrophysics Jeremy Sakstein Institute of Cosmology and Gravitation, Portsmouth Department of Applied Mathematics and Theoretical Physics, University of Cambridge 9 th May 2016 Why
Recent Progress on Curvature Squared Supergravities in Five and Six Dimensions
Recent Progress on Curvature Squared Supergravities in Five and Six Dimensions Mehmet Ozkan in collaboration with Yi Pang (Texas A&M University) hep-th/1301.6622 April 24, 2013 Mehmet Ozkan () April 24,
The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions
The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions Adalto R. Gomes Universidade Federal do Maranhão UFMA Based on a collaboration with Luca Amendola, Heidelberg
Cosmology in generalized Proca theories
3-rd Korea-Japan workshop on dark energy, April, 2016 Cosmology in generalized Proca theories Shinji Tsujikawa (Tokyo University of Science) Collaboration with A.De Felice, L.Heisenberg, R.Kase, S.Mukohyama,
Formation and Evaporation of Regular Black Holes in New 2d Gravity BIRS, 2016
Formation and Evaporation of Regular Black Holes in New 2d Gravity BIRS, 2016 G. Kunstatter University of Winnipeg Based on PRD90,2014 and CQG-102342.R1, 2016 Collaborators: Hideki Maeda (Hokkai-Gakuen
Probing alternative theories of gravity with Planck
Probing alternative theories of gravity with Planck Andrea Marchini Sapienza - University of Rome based on Updated constraints from the Planck experiment on modified gravity:prd88,027502 In collaboration
Holographic self-tuning of the cosmological constant
Holographic self-tuning of the cosmological constant Francesco Nitti Laboratoire APC, U. Paris Diderot IX Aegean Summer School Sifnos, 19-09-2017 work with Elias Kiritsis and Christos Charmousis, 1704.05075
Dark Energy & General Relativity «Some theoretical thoughts»
IAS workshop 24/11/2008 Dark Energy & General Relativity «Some theoretical thoughts» Jean-Philippe UZAN Cosmological models Theoretical physics Principles Local law of nature Extrapolations Cosmology models
NONLOCAL MODIFIED GRAVITY AND ITS COSMOLOGY
NONLOCAL MODIFIED GRAVITY AND ITS COSMOLOGY Branko Dragovich http://www.ipb.ac.rs/ dragovich email: dragovich@ipb.ac.rs Institute of Physics, University of Belgrade, and Mathematical Institute SANU Belgrade,
Black Holes in Four and More Dimensions
Black Holes in Four and More Dimensions Jutta Kunz Institute of Physics CvO University Oldenburg International Workshop on In-Medium Effects in Hadronic and Partonic Systems Obergurgl, Austria, February