Einstein-Maxwell-Chern-Simons Black Holes
|
|
- Silvester Barber
- 6 years ago
- Views:
Transcription
1 .. 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 Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
2 . Outline Outline. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
3 . Outline Outline. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
4 . Outline Outline. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
5 . Outline Outline. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
6 . Outline Introduction. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
7 Introduction. Generalization of D = 4 Black Holes: D > 4 Tangherlini (1963) Myers and Perry (1986) mmmm static mmmm mmmn rotating mmmn D = 4 Schwarzschild Kerr (M) (M, J) D > 4 Tangherlini Myers-Perry (M) (M, J 1,..., J N ) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
8 Introduction. Generalization of D = 4 Black Holes: D > 4 Tangherlini (1963) Myers and Perry (1986) mmmm static mmmm mmmn rotating mmmn D = 4 Schwarzschild Kerr (M) (M, J) D > 4 Tangherlini Myers-Perry (M) (M, J 1,..., J N ) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
9 Introduction. Generalization of D = 4 Black Holes: D > 4 Tangherlini (1963) Myers and Perry (1986) mmmm static mmmm mmmn rotating mmmn D = 4 Schwarzschild Kerr (M) (M, J) D > 4 Tangherlini Myers-Perry (M) (M, J 1,..., J N ) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
10 Introduction. Myers-Perry Black Holes Myers and Perry 1986 D: dimension of space-time D 1 N: number of independent angular momenta J i : N 2 N: number of independent planes x 3 ϕ 2 (x 3, x 4 ) x 4 θ (x 1, x 2 ) x 2 ϕ 1 x 1 example: D = 5, N = 2 Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
11 Introduction. Myers-Perry Black Holes metric Frolov and Kubiznak (2007) ds 2 D,MP = dt 2 ΠF N + Π mr 2 ε dr2 + (r 2 + a 2 i )(dµ 2 i + µ 2 i dφ 2 i ) + mr2 ε ΠF F 1 ( i=1 dt i=1 ) 2 N a i µ 2 i dφ i + εr 2 dν 2 i=1 N a 2 N i µ2 i r 2 + a 2, Π = (r 2 + a 2 i ) i i=1 N µ 2 i + εν 2 = 1 i=1 coordinate ν only in even dimensions: odd D : ε = 0 even D : ε = 1 mass M and angular momenta J i : M = m (1 + (D 3)) A(S D 2 ) J i = 2m a i A(S D 2 ), i = 1,..., N Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
12 Introduction. Myers-Perry Black Holes metric in odd D: a i = a ds 2 D,MP = dt 2 + ΠF Π mr 2 dr2 + + mr2 ΠF ( dt N (r 2 + a 2 )(dµ 2 i + µ 2 i dφ 2 i ) i=1 ) 2 N aµ 2 i dφ i i=1 F 1 N i=1 a 2 µ 2 i r 2 + a 2, N Π = (r 2 + a 2 ) i=1 enhanced symmetry: U(1) N U(N) factorization of angular coordinates Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
13 Introduction. Myers-Perry Black Holes: Domain of Existence D = 5: domain of existence is bounded j j 1 scaled angular momenta j 1 = J 1 /M (D 2)/(D 3) j 2 = J 2 /M (D 2)/(D 3) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
14 Introduction. Myers-Perry Black Holes: Domain of Existence D = 5: domain of existence is bounded j j 1 scaled angular momenta D = 6: domain of existence is unbounded on axes: for J 1 = J, J 2 = 0 for J 1 = 0, J 2 = J j 1 = J 1 /M (D 2)/(D 3) j 2 = J 2 /M (D 2)/(D 3) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
15 Introduction. Myers-Perry Black Holes: ds/ads Gibbons, Lu, Page and Pope (2004) ( )2 N 2µ ai ρ2i dϕi ds = W (1 + Λ r )dt + W dt U Ξi i=1 ( ) ) N ( 2 r + a2i U + dr2 + ϵ r2 dy 2 + (dρ2i + ρ2i dϕ2i ) Z 2µ Ξ i i=1 (N ( )2 r 2 + a2 ) Λ i 2 ρi dρi + ϵr ydy Ξi W (1 + Λ r2 ) i=1 Λ = 2Λ, Ξi = 1 Λ a2i (D 1)(D 2) N (1 + Λ r2 ) 2 (r + a2i ) r2 ϵ i=1 ) ( N Z a2i ρ2i U= 1 r2 + a2i 1 + Λ r2 i=1 W = ϵy 2 + N ρ2i, Ξ i=1 i Jutta Kunz (Universita t Oldenburg) Z= EMCS Black Holes Frankfurt, July / 35
16 . Outline Asymptotically Flat EMCS Black Holes. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
17 Asymptotically Flat EMCS Black Holes. D = 5 Einstein-Maxwell-Chern-Simons Theory Jutta Kunz (Universita t Oldenburg) EMCS Black Holes Frankfurt, July / 35
18 Asymptotically Flat EMCS Black Holes. D = 5 Einstein-Maxwell-Chern-Simons Theory In odd dimensions D = 2n + 1 the Einstein-Maxwell action may be supplemented by a AF n Chern-Simons term. D = 5 Einstein-Maxwell-Chern-Simons action S = 1 { g (R Fµν F µν ) 2λ 16πG εmnpqr A m F np F qr }{{} Chern Simons } d 5 x Chern-Simons coupling constant λ λ = 0: λ = 1: Einstein-Maxwell theory bosonic sector of minimal D = 5 supergravity λ > 1 Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
19 Asymptotically Flat EMCS Black Holes. D = 5 Einstein-Maxwell-Chern-Simons Theory coupled set of field equations Einstein equations G µν = 2 (F µρ F ρν 14 ) F ρσf ρσ Maxwell Chern-Simons equations unchanged w.r.t. Einstein-Maxwell ν F µν + λ 2 3 ϵµναβγ F να F βγ = 0. breaking of Q Q symmetry if λ 0 Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
20 Asymptotically Flat EMCS Black Holes. D = 5 Einstein-Maxwell-Chern-Simons Theory Ansätze: J 1 = J 2 = J (cohomogeneity-1) metric ds 2 = F 1 (r)dr F 2(r)(σ σ 2 2) F 3(r) ( σ 3 2ω(r)dt ) 2 F0 (r)dt 2, gauge potential A = a 0 (r)dt + a φ (r) 1 2 σ 3, angular dependence left-invariant 1-forms σ i on S 3 σ 1 = cos ψdθ + sin ψ sin θdϕ σ 2 = sin ψdθ + cos ψ sin θdϕ σ 3 = dψ + cos θdϕ θ, ϕ and ψ: Euler angles on S 3 (0 θ π, 0 ϕ 2π, 0 ψ 4π) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
21 . Outline Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
22 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory. Einstein-Maxwell Black Holes higher dimensional black holes? no closed form solutions except for Tangherlini perturbative solutions small J small Q extremal near horizon solutions odd D, equal J numerical solutions odd D, equal J a single J Jutta Kunz (Universita t Oldenburg) EMCS Black Holes Frankfurt, July / 35
23 Asymptotically Flat EMCS Black Holes. Einstein-Maxwell Black Holes D = 5 Einstein-Maxwell Theory Gauntlett, Myers, Townsend (1999) first law mass formula dm = T ds + 2ΩdJ + ΦdQ D 3 D 2 M = 2κA H + N i=1 Ω i J i + D 3 D 2 Φ HQ M: mass T : surface gravity S: area Ω: angular velocity J: angular momentum Φ: horizon potential Q: charge Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
24 Asymptotically Flat EMCS Black Holes. Einstein-Maxwell Black Holes gyromagnetic ratio g: D = 5 Einstein-Maxwell Theory µ mag = g QJ 2M Aliev and Frolov (2004), Aliev (2006) perturbative result in lowest order: g = D 2 Navarro-Lérida (2010) perturbative result in higher order: g D 2 g/(d-2) D 7D 9D 3rd order extremal black holes g D 2 = 1+ 1 ( ) 2 Q M Q/M Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
25 Asymptotically Flat EMCS Black Holes. Near Horizon Solutions D = 5 Einstein-Maxwell Theory Kunduri, Lucietti (2013) Blázquez-Salcedo, J.K., Navarro-Lérida (2013) near-horizon geometry of extremal black holes: AdS 2 S 3 metric gauge potential ds 2 = v 1 ( dr2 r 2 r2 dt 2 ) + v 2 [ σ σ v 3 (σ 3 krdt) 2] A µ dx µ = q 1 rdt + q 2 (σ 3 krdt) σ 1 = cos ψdθ + sin ψ sin θdϕ, σ 2 = sin ψdθ + cos ψ sin θdϕ, σ 3 = dψ + cos θdϕ Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
26 Asymptotically Flat EMCS Black Holes. Near Horizon Solutions D = 5 Einstein-Maxwell Theory angular momentum area relation for EM black holes vs scaled charge MP branch, 5D RN branch, 5D MP branch, 7D RN branch, 7D MP branch, 9D RN branch, 9D MP branch, 11D RN branch, 11D equal magnitude angular momenta EM in D dimensions 2 solutions 1st solution: A H /J 0.6 J = 2(D 3)A H Q/J (D-3)/(D-2) MP branch 2nd solution: J = (D 1)J H RN branch Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
27 Asymptotically Flat EMCS Black Holes. Near Horizon Solutions D = 5 Einstein-Maxwell Theory angular momentum area relation for EM black holes vs scaled charge MP branch, 5D RN branch, 5D MP branch, 7D RN branch, 7D MP branch, 9D RN branch, 9D MP branch, 11D RN branch, 11D equal magnitude angular momenta EM in D dimensions 2 solutions 1st solution: J H /J 0.50 J = 2(D 3)A H Q/J (D-3)/(D-2) MP branch 2nd solution: J = (D 1)J H RN branch Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
28 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory. Near Horizon and Global Solutions A H Q scaled area of EM black holes vs scaled charge M (D 2)/(D 3) M A H /M (D-2)/(D-3) Q/M Extremal D=5 Extremal D=7 Extremal D=9 Static D=5 Static D=7 Static D=9 equal magnitude angular momenta D dimensions globally realized: MP branch: small Q/M RN branch: large Q/M switch: matching point Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
29 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory. Near Horizon and Global Solutions J scaled angular momenta of EM black holes vs scaled charge M (D 2)/(D 3) J/M (D-2)/(D-3) Q/M Extremal D=5 Extremal D=7 Extremal D=9 Static D=5 Static D=7 Static D=9 equal magnitude angular momenta D dimensions globally realized: MP branch: small Q/M RN branch: large Q/M switch: matching point Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
30 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory. Near Horizon and Global Solutions D = 5 extremal black holes in EM theory: λ = 0 J /M 3/2 J 1 = J 2, λ= λ= /2 Q/M boundary of domain of existence non-extremal bhs inside naked singularities outside J = 0: static black holes RN black holes extremal RN on the boundary λ = 0 symmetry q q Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
31 . Outline Asymptotically Flat EMCS Black Holes D = 5 minimal supergravity. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
32 Asymptotically Flat EMCS Black Holes D = 5 minimal supergravity. Einstein-Maxwell-Chern-Simons Black Holes: λ = 1 Breckenridge, Myers, Peet and Vafa (1997) Chong, Cveti c, Lü and Pope (2005) extremal λ = 1 EMCS black holes: J /M 3/ J 1 = J 2, λ=0, 1 λ=0 λ= /2 Q/M boundary of domain of existence non-extremal bhs inside naked singularities outside J = 0: static black holes RN black holes extremal RN on the boundary λ 0 symmetry q q broken Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
33 Asymptotically Flat EMCS Black Holes D = 5 minimal supergravity. Einstein-Maxwell-Chern-Simons Black Holes: λ = 1 Breckenridge, Myers, Peet and Vafa (1997) Chong, Cveti c, Lü and Pope (2005) extremal λ = 1 EMCS black holes: J /M 3/ J 1 = J 2, λ=0, 1 λ=0 λ= /2 Q/M vertical wall BMPV solutions Q is kept fixed J increases M remains constant first law dm = T ds + Ω i dj i + ΦdQ extremal: T = 0 Q fixed: dq = 0 M fixed: dm = 0??? Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
34 Asymptotically Flat EMCS Black Holes D = 5 minimal supergravity. Einstein-Maxwell-Chern-Simons Black Holes: λ = 1 Breckenridge, Myers, Peet and Vafa (1997) Chong, Cveti c, Lü and Pope (2005) extremal λ = 1 EMCS black holes: J /M 3/ J 1 = J 2, λ=0, 1 λ=0 λ= /2 Q/M horizon angular velocites vanish: Ω i = 0, J = 0 angular momentum is stored in the Maxwell field negative fraction of the angular momentum is stored behind the horizon the effect of rotation is to deform the horizon into a squashed 3-sphere Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
35 . Outline Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
36 Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. Einstein-Maxwell-Chern-Simons Black Holes: λ > 1 J.K., Navarro-Lérida (2006) λ=1.5 λ=1 J 1 = J 2 Ω= λ=2 J 1 = J 2, λ=0, 1, 2 λ=1 Ω=0 J /M 3/ λ=0 J /M 3/ λ= /2 Q/M black holes with Ω = 0, J 0 black holes with Ω < 0, J > /2 Q/M non-extremal counter-rotating (shaded area) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
37 Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. Einstein-Maxwell-Chern-Simons Black Holes: λ > 1 λ > 2 EMCS black holes r H =0.1 r H =0.5 J 1 = J 2, λ=3, Q=-1 non-extremal black holes black holes are not uniquely determined by M, J i, Q J M non-uniqueness of 5D black holes with horizon topology of a sphere S 3 extremal black holes angular momentum vs mass Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
38 Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. Extremal EMCS Black Holes: λ > 2 j Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2014) domain of existence: λ = λ=5 extremal λ=5 extremal, static extremal black holes: boundary of domain of existence inside the domain of existence many branches J = 0 non-static black holes sequence of pairs q ns > q s limit q extremal RN: q s Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
39 Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. Extremal EMCS Black Holes: λ > 2 M Q>0 global Q<0 global branches for fixed Q: λ = 5 C [1,2] C [1,2] C [3,4] C [3,4] (B [2,3], B * [2,3] ) (B [2,3], B* [2,3] ) n=3 n>6 (B [1,2], B * [1,2] ) n=2 (B [1,2], B* [1,2] ) n= J n=6 n=5 n=4 0 extremal black holes: J = 0 non-static black holes sequence of pairs labelled by integer n limit n : extremal RN branchpoints B and cusps C nonuniqueness Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
40 Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. Extremal EMCS Black Holes: λ > 2 A H horizon area: λ = 5, Q fixed C nh Q>0 global Q<0 global C [1,2] C [1,2] C [3,4] C [3,4] B [1,2] B [1,2] n=1, 2,... B * [1,2] B * [1,2] Q>0 near horizon Q<0 near horizon J C nh extremal black holes: J = 0 non-static black holes same area extremal RN isolated near horizon vs global solutions zero global bh one global bh many global bh Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
41 Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. Extremal EMCS Black Holes: λ > 2 how do the solutions on these branches differ? what is the origin of the branch structure? Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
42 Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. Radial Excitations of Extremal EMCS Black Holes 0.50 gauge field function a φ n=7 n=6 n=5 n=4 n=3 n= a ϕ λ=5 n= /3 log 10 (r/a H ) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
43 Asymptotically Flat EMCS Black Holes D = 5 EMCS theory: λ 1. Radial Excitations of Extremal EMCS Black Holes 0 metric function ω -2-4 log 10 ( ω ) -6 1 node -8 2 nodes 3 nodes 4 nodes 5 nodes 6 nodes nodes 8 nodes 9 nodes 10 nodes log 10 (x) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
44 . Outline EMCS Solutions with AdS Asymptotics. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
45 EMCS Solutions with AdS Asymptotics. Anti-de Sitter space Jutta Kunz (Universita t Oldenburg) EMCS Black Holes Frankfurt, July / 35
46 EMCS Solutions with AdS Asymptotics. Adding a negative cosmological constant Λ D = 5 Einstein-Maxwell-Chern-Simons action 1 { ( g S = R + 12 ) 16πG 5 L 2 F µνf µν 2λ } 3 3 εmnpqr A m F np F qr d 5 x cosmological constant Λ = 6/L 2 Chern-Simons coupling constant λ λ = 0: λ = 1: Einstein-Maxwell theory bosonic sector of D = 5 gauged supergravity λ 1 Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
47 . Outline EMCS Solutions with AdS Asymptotics Charged solutions. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
48 EMCS Solutions with AdS Asymptotics Charged solutions. Charged solutions in gauged supergravity: λ = 1 Chong, Cveti c, Lü and Pope (2005): trial and error 2 independent angular momenta, g = 1/L Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
49 EMCS Solutions with AdS Asymptotics Charged solutions. Charged EMCS solutions: λ 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) small λ global (non-extremal) J H global (extremal) + near horizon P 2 Gap near horizon P horizon angular momentum J H vs angular momentum J J Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
50 EMCS Solutions with AdS Asymptotics Charged solutions. Charged EMCS solutions: λ 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) small λ Near-horizon, λ=0.1 Global, λ=0.1 Near-horizon, λ=0.025 Global, λ=0.025 Near-horizon, EM-AdS Global, EM-AdS Q> Near-horizon, λ=0.5 Global, λ=0.5 Near-horizon, λ=0.1 Global, λ=0.1 Near-horizon, EM-AdS Global, EM-AdS Q<0 J H J H Gap Gap J J Q > 0 Q < 0 dots, triangles: limiting solutions, squares: critical solutions A H = 0 Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
51 EMCS Solutions with AdS Asymptotics Charged solutions. Charged EMCS solutions: λ 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) large λ 0.2 n=1 n=2 n=3 n=4 n=5 n=6 3 0 AdS boundary a ϕ 0 F 2 horizon horizon r/(1+r) AdS boundary -6 n=1 n=2 n=3 n=4 n=5 n=6 RN-AdS r/(1+r) Q < 0 Q < 0 magnetic gauge potential a φ invariant F 2 = F µν µν Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
52 EMCS Solutions with AdS Asymptotics Charged solutions. Charged EMCS solutions: λ 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) horizon area A H vs charge Q: temperature T H plot Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
53 . Outline EMCS Solutions with AdS Asymptotics Magnetized solutions. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
54 EMCS Solutions with AdS Asymptotics Magnetized solutions. Static purely magnetic solutions: λ = 0 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2016) r : a φ c m Φ m = 1 F = 1 4π 2 c m S D=7 D=5 50 D=7-3 D=9 M µ 0 D= D= c m c m mass M vs flux parameter c m magnetic moment µ vs c m Solitons Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
55 EMCS Solutions with AdS Asymptotics Magnetized solutions. Static purely magnetic solutions: λ = 0 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2016) Black holes in D = soliton limit 1 c m =0 c m =1.5 c m =2 c m =2.5 c m =3 Type I Type II M A H c m =0 c m =1.5 c m =2 singular limit c m =2.5 c m =3 Type I Type II T H singular limit soliton limit T H mass M vs temperature T H horizon area A H vs T H type I: M, A H increase with T H type II: M, A H decrease with T H type I: for all c m type II: for c m < c m Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
56 EMCS Solutions with AdS Asymptotics Magnetized solutions. Static purely magnetic solutions: λ = 0 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2016) 10 domain of existence: D = 5 Type I black holes 0 M Type II black holes -10 singular limit solitons c m Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
57 EMCS Solutions with AdS Asymptotics Magnetized solutions. Rotating magnetized solutions: λ = 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) solitons: mass M, angular momentum J and charge Q (R) vs c m L=1 3Q (R) M -J c m single parameter no upper bound on c m no radial excitations for λ = 1 radial excitations for λ > 1? c m 1 3 Q = Q(R) = 1 2 S 3 ( F + 2λ ) 3 3 A F, J = λπ 3 3 c3 m = Φ m Q (R) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
58 EMCS Solutions with AdS Asymptotics Magnetized solutions. Rotating magnetized solutions: λ = 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) black holes: mass M vs temperature T H M c m = 0 c m = 0.2 c m = -0.2 c m = 0.33 c m = c m = 0.66 c m = parameters: J, Q (R), c m c m 0: relevant for small T H only large c m : black holes thermodynamically stable rotating J = 0 black holes T H J = 0.003, Q (R) = Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
59 EMCS Solutions with AdS Asymptotics Magnetized solutions. Rotating magnetized solutions: λ = 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) black holes: area A H vs temperature T H A H c m = 0 c m = 0.2 c m = -0.2 c m = 0.33 c m = c m = 0.66 c m = parameters: J, Q (R), c m c m 0: relevant for small T H only large c m : black holes thermodynamically stable rotating J = 0 black holes T H J = 0.003, Q (R) = Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
60 EMCS Solutions with AdS Asymptotics Magnetized solutions. Rotating magnetized solutions: λ = 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) T H, M, c m T H, c m, A H stationary J = 0 black holes L = 1, Q (R) = Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
61 EMCS Solutions with AdS Asymptotics Magnetized solutions. Rotating magnetized solutions: λ = 1 Blázquez-Salcedo, J.K., Navarro-Lérida, Radu (2017) T H, Ω H, c m T H, R(r H ), c m stationary J = 0 black holes L = 1, Q (R) = Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
62 . Outline EMCS Solutions with AdS Asymptotics Magnetized squashed solutions. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
63 EMCS Solutions with AdS Asymptotics. Squashed solitons: λ = 1 Cassani and Martelli (2014) Magnetized squashed solutions boundary metric: squashed S 3 sphere ds 2 (bdry) = L2 dω 2 (v) dt2, dω 2 (v) = 1 ( dθ 2 + sin 2 θdϕ 2 + (dψ + v cos θdϕ) 2) 4 v: control parameter M susy black holes susy solitons -1 J Gutowski-Reall black holes 2.5 Q squashed susy solitons ( 5 M = πl v v ) 864 v4 5 J = πl3 27 Q = 2πL2 9 3 ( v 2 1 ) 3 ( v 2 1 ) 2 Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
64 EMCS Solutions with AdS Asymptotics Magnetized squashed solutions. Magnetized squashed solutions: λ = 1 work in progress boundary metric: squashed S 3 sphere ds 2 (bdry) = L2 dω 2 (v) dt2, dω 2 (v) = 1 ( dθ 2 + sin 2 θdϕ 2 + (d 4 ψ + v cos θdϕ) 2) v: control parameter M susy black holes susy solitons -1 J Gutowski-Reall black holes 2.5 Q 5 nonextremal black holes event horizon of spherical topology, no pathologies characterization: M, Q, J, c m r H 0: squashed spinning charged solitons J = Φ m Q. Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
65 EMCS Solutions with AdS Asymptotics Magnetized squashed solutions. Magnetized squashed solutions: λ = 1 work in progress boundary metric: squashed S 3 sphere ds 2 (bdry) = L2 dω 2 (v) dt2, dω 2 (v) = 1 ( dθ 2 + sin 2 θdϕ 2 + (d 4 ψ + v cos θdϕ) 2) v: control parameter log 10 A H J=1.07, Q=3.49 J=0.8, Q=2.3 J=0.8, Q=1.21 J=0.6, Q=1.21 J=0.61, Q=1.21 susy black hole log 10 M 0.6 J=1.07, Q=3.49 J=0.8, Q=2.3 J=0.8, Q=1.21 J=0.6, Q=1.21 J=0.61, Q=1.21 susy black hole susy solitons susy solitons T H T H black holes v = 1.65, c = 1, L = 1 Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
66 EMCS Solutions with AdS Asymptotics Magnetized squashed solutions. Magnetized squashed solutions: λ = 1 work in progress boundary metric: squashed S 3 sphere ds 2 (bdry) = L2 dω 2 (v) dt2, dω 2 (v) = 1 ( dθ 2 + sin 2 θdϕ 2 + (d 4 ψ + v cos θdϕ) 2) v: control parameter 2 J=1.07, Q=3.49 J=0.8, Q=2.3 J=0.8, Q=1.21 J=0.6, Q=1.21 J=0.61, Q=1.21 susy black hole 1.6 Ω H 0 susy solitons ε 1.3 J=1.07, Q=3.49 J=0.8, Q=2.3 J=0.8, Q=1.21 J=0.6, Q=1.21 J=0.61, Q=1.21 susy black hole susy solitons T H T H black holes v = 1.65, c = 1, L = 1 Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
67 EMCS Solutions with AdS Asymptotics Magnetized squashed solutions. Magnetized squashed solutions: λ = 1 work in progress boundary metric: squashed S 3 sphere ) 1( 2 ds2(bdry) = L2 dω2(v) dt2, dω2(v) = dθ + sin2 θdϕ2 + (dψ + v cos θdϕ)2 4 v: control parameter black holes Jutta Kunz (Universita t Oldenburg) EMCS Black Holes Frankfurt, July / 35
68 EMCS Solutions with AdS Asymptotics Magnetized squashed solutions. Magnetized squashed solutions: λ = 1 work in progress boundary metric: squashed S 3 sphere ds 2 (bdry) = L2 dω 2 (v) dt2, dω 2 (v) = 1 ( dθ 2 + sin 2 θdϕ 2 + (d 4 ψ + v cos θdϕ) 2) v: control parameter black holes Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
69 EMCS Solutions with AdS Asymptotics Magnetized squashed solutions. Magnetized squashed solutions: λ = 1 work in progress boundary metric: squashed S 3 sphere ds 2 (bdry) = L2 dω 2 (v) dt2, dω 2 (v) = 1 ( dθ 2 + sin 2 θdϕ 2 + (d 4 ψ + v cos θdϕ) 2) v: control parameter 10 3 susy black holes 10 2 Gutkowski-Real susy black holes (2004) round sphere: v = 1 no magnetization: c m = 0 M susy solitons -1 J Gutowski-Reall black holes 2.5 Q 5 M = πl2 216 (3α2 1)( α α 4 ) + C J = πl3 216 (1 4α2 ) 2 (7 + 8α 2 ) Q = πl (4α2 1)(5 + 4α 2 ) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
70 EMCS Solutions with AdS Asymptotics Magnetized squashed solutions. Magnetized squashed solutions: λ = 1 work in progress boundary metric: squashed S 3 sphere ds 2 (bdry) = L2 dω 2 (v) dt2, dω 2 (v) = 1 ( dθ 2 + sin 2 θdϕ 2 + (d 4 ψ + v cos θdϕ) 2) v: control parameter 10 3 susy black holes Gutowski-Reall black holes M susy solitons J Q 1 0 new susy black holes ( 7913 M = πl v v ) 864 v4 ( J = πl v v4 1 ) 27 v6 5 Q = π 3L ( v v 4) A H = 7π 2 L c m = ± L 3 ( 1 v 2 ) Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
71 . Outline Conclusion and Outlook. 1 Introduction. 2 Asymptotically Flat EMCS Black Holes D = 5 Einstein-Maxwell Theory D = 5 minimal supergravity D = 5 EMCS theory: λ 1. 3 EMCS Solutions with AdS Asymptotics Charged solutions Magnetized solutions Magnetized squashed solutions. 4 Conclusion and Outlook Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
72 . Conclusions Conclusion and Outlook Einstein-Maxwell-Chern-Simons black holes: D = 5 M Q>0 global Q<0 global C [1,2] C [1,2] C [3,4] C [3,4] (B [2,3], B * [2,3] ) (B [2,3], B* [2,3] ) n=3 n>6 (B [1,2], B * [1,2] ) n=2 (B [1,2], B* [1,2] ) n= J mass vs angular momentum n=6 n=5 n=4 0 black holes with surprising properties non-uniqueness Ω = 0, J 0 non-static J = 0 sequences of radially excited extremal black holes... questions in which theories? in D = 4? consequences?... Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
73 . Conclusions Conclusion and Outlook Einstein-Maxwell-Chern-Simons AdS solutions: D = 5 10 black holes and solitons c m = 0: many properties retained c m 0: new solitons M 0-10 Type I black holes Type II black holes singular limit solitons c m mass vs magnetic flux new black holes J = Φ mq squashed magnetized solutions new solitons new black holes... questions domain of existence?... Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
74 Conclusion and Outlook. Higher Dimensions: D 6 Dias, Figueras, Monteiro, Santos, Emparan (2009) unstable modes of Myers-Perry black holes: D 6 Jutta Kunz (Universita t Oldenburg) EMCS Black Holes Frankfurt, July / 35
75 Conclusion and Outlook. Higher Dimensions: D 6 Emparan, Figueras (2010) D 6 horizon area vs. angular momentum at fixed mass Jutta Kunz (Universita t Oldenburg) EMCS Black Holes Frankfurt, July / 35
76 . THANKS Conclusion and Outlook Jose Francisco Eugen Blázquez-Salcedo Navarro-Lérida Radu Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
77 . THANKS Conclusion and Outlook Thank you very much for your attention Jutta Kunz (Universität Oldenburg) EMCS Black Holes Frankfurt, July / 35
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
More informationJose Luis Blázquez Salcedo
Physical Review Letters 112 (2014) 011101 Jose Luis Blázquez Salcedo In collaboration with Jutta Kunz, Eugen Radu and Francisco Navarro Lérida 1. Introduction: Ansatz and general properties 2. Near-horizon
More informationJose Luis Blázquez Salcedo
Jose Luis Blázquez Salcedo In collaboration with Jutta Kunz, Francisco Navarro Lérida, and Eugen Radu GR Spring School, March 2015, Brandenburg an der Havel 1. Introduction 2. General properties of EMCS-AdS
More informationCharged Rotating Black Holes in Higher Dimensions
Charged Rotating Black Holes in Higher Dimensions Francisco Navarro-Lérida1, Jutta Kunz1, Dieter Maison2, Jan Viebahn1 MG11 Meeting, Berlin 25.7.2006 Outline Introduction Einstein-Maxwell Black Holes Einstein-Maxwell-Dilaton
More informationBlack 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
More informationRotating Charged Black Holes in D>4
Rotating Charged Black Holes in D>4 Marco Caldarelli LPT Orsay & CPhT Ecole Polytechnique based on arxiv:1012.4517 with R. Emparan and B. Van Pol Orsay, 19/01/2010 Summary The many scales of higher D black
More informationBlack hole near-horizon geometries
Black hole near-horizon geometries James Lucietti Durham University Imperial College, March 5, 2008 Point of this talk: To highlight that a precise concept of a black hole near-horizon geometry can be
More informationThe abundant richness of Einstein-Yang-Mills
The abundant richness of Einstein-Yang-Mills Elizabeth Winstanley Thanks to my collaborators: Jason Baxter, Marc Helbling, Eugen Radu and Olivier Sarbach Astro-Particle Theory and Cosmology Group, Department
More informationExtremal black holes and near-horizon geometry
Extremal black holes and near-horizon geometry James Lucietti University of Edinburgh EMPG Seminar, Edinburgh, March 9 1 Higher dimensional black holes: motivation & background 2 Extremal black holes &
More informationBlack hole instabilities and violation of the weak cosmic censorship in higher dimensions
Black hole instabilities and violation of the weak cosmic censorship in higher dimensions Pau Figueras School of Mathematical Sciences, Queen Mary University of London w/ Markus Kunesch, Luis Lehner and
More informationGeneral Relativity and Cosmology Mock exam
Physikalisches Institut Mock Exam Universität Bonn 29. June 2011 Theoretische Physik SS 2011 General Relativity and Cosmology Mock exam Priv. Doz. Dr. S. Förste Exercise 1: Overview Give short answers
More informationKerr black hole and rotating wormhole
Kerr Fest (Christchurch, August 26-28, 2004) Kerr black hole and rotating wormhole Sung-Won Kim(Ewha Womans Univ.) August 27, 2004 INTRODUCTION STATIC WORMHOLE ROTATING WORMHOLE KERR METRIC SUMMARY AND
More informationCosmological constant is a conserved charge
Cosmological constant is a conserved Kamal Hajian Institute for Research in Fundamental Sciences (IPM) In collaboration with Dmitry Chernyavsky (Tomsk Polytechnic U.) arxiv:1710.07904, to appear in Classical
More informationMass and thermodynamics of Kaluza Klein black holes with squashed horizons
Physics Letters B 639 (006 354 361 www.elsevier.com/locate/physletb Mass and thermodynamics of Kaluza Klein black holes with squashed horizons Rong-Gen Cai ac Li-Ming Cao ab Nobuyoshi Ohta c1 a Institute
More informationON THE BLACK HOLE SPECIES
Paris ON THE BLACK HOLE SPECIES (by means of natural selection) Maria J. Rodriguez 16.07.09 Dumitru Astefanesei and MJR ( to appear) Marco Calderelli, Roberto Emparan and MJR ( 0806.1954 [hep-th] ) Henriette
More informationBPS Black holes in AdS and a magnetically induced quantum critical point. A. Gnecchi
BPS Black holes in AdS and a magnetically induced quantum critical point A. Gnecchi June 20, 2017 ERICE ISSP Outline Motivations Supersymmetric Black Holes Thermodynamics and Phase Transition Conclusions
More informationDilatonic Black Saturn
Dilatonic Black Saturn Saskia Grunau Carl von Ossietzky Universität Oldenburg 7.5.2014 Introduction In higher dimensions black holes can have various forms: Black rings Black di-rings Black saturns...
More informationarxiv:hep-th/ v3 25 Sep 2006
OCU-PHYS 46 AP-GR 33 Kaluza-Klein Multi-Black Holes in Five-Dimensional arxiv:hep-th/0605030v3 5 Sep 006 Einstein-Maxwell Theory Hideki Ishihara, Masashi Kimura, Ken Matsuno, and Shinya Tomizawa Department
More informationGlobal and local problems with. Kerr s solution.
Global and local problems with Kerr s solution. Brandon Carter, Obs. Paris-Meudon, France, Presentation at Christchurch, N.Z., August, 2004. 1 Contents 1. Conclusions of Roy Kerr s PRL 11, 237 63. 2. Transformation
More informationWHY BLACK HOLES PHYSICS?
WHY BLACK HOLES PHYSICS? Nicolò Petri 13/10/2015 Nicolò Petri 13/10/2015 1 / 13 General motivations I Find a microscopic description of gravity, compatibile with the Standard Model (SM) and whose low-energy
More informationDynamical compactification from higher dimensional de Sitter space
Dynamical compactification from higher dimensional de Sitter space Matthew C. Johnson Caltech In collaboration with: Sean Carroll Lisa Randall 0904.3115 Landscapes and extra dimensions Extra dimensions
More informationModelling the evolution of small black holes
Modelling the evolution of small black holes Elizabeth Winstanley Astro-Particle Theory and Cosmology Group School of Mathematics and Statistics University of Sheffield United Kingdom Thanks to STFC UK
More informationMy talk Two different points of view:
Shin Nakamura (Dept. Phys. Kyoto Univ.) Reference: S.N., Hirosi Ooguri, Chang-Soon Park, arxiv:09.0679[hep-th] (to appear in Phys. Rev. D) ( k B = h= c=) My talk Two different points of view: rom the viewpoint
More informationJason Doukas Yukawa Institute For Theoretical Physics Kyoto University
1/32 MYERS-PERRY BLACK HOLES: BEYOND THE SINGLE ROTATION CASE Jason Doukas Yukawa Institute For Theoretical Physics Kyoto University Lunch meeting FEB 02, 2011 2/32 Contents 1. Introduction. 1.1 Myers
More informationÜbungen 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
More informationExpanding plasmas from Anti de Sitter black holes
Expanding plasmas from Anti de Sitter black holes (based on 1609.07116 [hep-th]) Giancarlo Camilo University of São Paulo Giancarlo Camilo (IFUSP) Expanding plasmas from AdS black holes 1 / 15 Objective
More informationWhere is the PdV term in the first law of black-hole thermodynamics?
Where is the PdV term in the first law of black-hole thermodynamics? Brian P Dolan National University of Ireland, Maynooth, Ireland and Dublin Institute for Advanced Studies, Ireland 9th Vienna Central
More informationAnalytic solutions of the geodesic equation in static spherically symmetric spacetimes in higher dimensions
Analytic solutions of the geodesic equation in static spherically symmetric spacetimes in higher dimensions Eva Hackmann 2, Valeria Kagramanova, Jutta Kunz, Claus Lämmerzahl 2 Oldenburg University, Germany
More informationBlack holes in N = 8 supergravity
Black holes in N = 8 supergravity Eighth Crete Regional Meeting in String Theory, Nafplion David Chow University of Crete 9 July 2015 Introduction 4-dimensional N = 8 (maximal) supergravity: Low energy
More informationOn 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
More informationMicrostate Geometries. Non-BPS Black Objects
Microstate Geometries and Non-BPS Black Objects Nick Warner Inaugural Workshop on Black Holes in Supergravity and M/Superstring Theory Penn State, September 10 th, 2010 Based upon work with I. Bena, N.
More informationReferences. S. Cacciatori and D. Klemm, :
References S. Cacciatori and D. Klemm, 0911.4926: Considered arbitrary static BPS spacetimes: very general, non spherical horizons, complicated BPS equations! G. Dall Agata and A. Gnecchi, 1012.3756 Considered
More informationSelf trapped gravitational waves (geons) with anti-de Sitter asymptotics
Self trapped gravitational waves (geons) with anti-de Sitter asymptotics Gyula Fodor Wigner Research Centre for Physics, Budapest ELTE, 20 March 2017 in collaboration with Péter Forgács (Wigner Research
More informationRotating Attractors - one entropy function to rule them all Kevin Goldstein, TIFR ISM06, Puri,
Rotating Attractors - one entropy function to rule them all Kevin Goldstein, TIFR ISM06, Puri, 17.12.06 talk based on: hep-th/0606244 (Astefanesei, K. G., Jena, Sen,Trivedi); hep-th/0507096 (K.G., Iizuka,
More informationarxiv: v1 [gr-qc] 7 Jan 2018
Dynamics of test particles in the five-dimensional Gödel spacetime Kevin Eickhoff 1, and Stephan Reimers 1, 1 Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany Dated: 8. April 2018 We
More informationHolographic Entanglement Entropy for Surface Operators and Defects
Holographic Entanglement Entropy for Surface Operators and Defects Michael Gutperle UCLA) UCSB, January 14th 016 Based on arxiv:1407.569, 1506.0005, 151.04953 with Simon Gentle and Chrysostomos Marasinou
More informationSpin and charge from space and time
Vienna University of Technology Manfried Faber Spin and charge from space and time in cooperation with Roman Bertle, Roman Höllwieser, Markus Jech, Alexander Kobushkin, Mario Pitschmann, Lukas Schrangl,
More informationIntegrability of five dimensional gravity theories and inverse scattering construction of dipole black rings
Integrability of five dimensional gravity theories and inverse scattering construction of dipole black rings Jorge V. Rocha CENTRA, Instituto Superior Técnico based on: arxiv:0912.3199 with P. Figueras,
More informationA Summary of the Black Hole Perturbation Theory. Steven Hochman
A Summary of the Black Hole Perturbation Theory Steven Hochman Introduction Many frameworks for doing perturbation theory The two most popular ones Direct examination of the Einstein equations -> Zerilli-Regge-Wheeler
More informationBlack 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
More informationLecture 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
More informationκ = f (r 0 ) k µ µ k ν = κk ν (5)
1. Horizon regularity and surface gravity Consider a static, spherically symmetric metric of the form where f(r) vanishes at r = r 0 linearly, and g(r 0 ) 0. Show that near r = r 0 the metric is approximately
More informationMagnetized black holes and black rings in the higher dimensional dilaton gravity
Magnetized black holes and black rings in the higher dimensional dilaton gravity arxiv:gr-qc/0511114v1 1 Nov 005 Stoytcho S. Yazadjiev Department of Theoretical Physics, Faculty of Physics, Sofia University,
More informationChapter 2 Black Holes in General Relativity
Chapter 2 Black Holes in General Relativity Abstract As a prelude to our study of quantum black holes, in this chapter we briefly review some of the key features of black holes in general relativity. We
More informationarxiv:hep-th/ v2 24 Sep 1998
Nut Charge, Anti-de Sitter Space and Entropy S.W. Hawking, C.J. Hunter and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom
More informationTHE 2D ANALOGUE OF THE REISSNER-NORDSTROM SOLUTION. S. Monni and M. Cadoni ABSTRACT
INFNCA-TH9618 September 1996 THE 2D ANALOGUE OF THE REISSNER-NORDSTROM SOLUTION S. Monni and M. Cadoni Dipartimento di Scienze Fisiche, Università di Cagliari, Via Ospedale 72, I-09100 Cagliari, Italy.
More informationarxiv: v2 [gr-qc] 1 Apr 2016
April 4, 2016 0:46 WSPC Proceedings - 9.75in x 6.5in main page 1 1 Black Holes in Higher Dimensions (Black Strings and Black Rings) Burkhard Kleihaus and Jutta Kunz Institut für Physik, Universität Oldenburg,
More informationQFT Corrections to Black Holes
Dedicated to the memory of Iaonnis Bakas QFT Corrections to Black Holes Hessamaddin Arfaei In collaboratin with J. Abedi, A. Bedroya, M. N. Kuhani, M. A. Rasulian and K. S. Vaziri Sharif University of
More informationTOPIC V BLACK HOLES IN STRING THEORY
TOPIC V BLACK HOLES IN STRING THEORY Lecture notes Making black holes How should we make a black hole in string theory? A black hole forms when a large amount of mass is collected together. In classical
More informationInstability of extreme black holes
Instability of extreme black holes James Lucietti University of Edinburgh EMPG seminar, 31 Oct 2012 Based on: J.L., H. Reall arxiv:1208.1437 Extreme black holes Extreme black holes do not emit Hawking
More informationBlack Holes. Jan Gutowski. King s College London
Black Holes Jan Gutowski King s College London A Very Brief History John Michell and Pierre Simon de Laplace calculated (1784, 1796) that light emitted radially from a sphere of radius R and mass M would
More informationAdS and Af Horndeski black hole solutions in four dimensions
AdS and Af Horndeski black hole solutions in four dimensions Physics and Mathematics Department, Universidad Austral de Chile December 17, 2014 (UACh) AdS and Af Horndeski black hole solutions December
More informationRadiation from the non-extremal fuzzball
adiation from the non-extremal fuzzball Borun D. Chowdhury The Ohio State University The Great Lakes Strings Conference 2008 work in collaboration with Samir D. Mathur (arxiv:0711.4817) Plan Describe non-extremal
More informationUniversal 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
More informationAsymptotic Quasinormal Frequencies for d Dimensional Black Holes
Asymptotic Quasinormal Frequencies for d Dimensional Black Holes José Natário (Instituto Superior Técnico, Lisbon) Based on hep-th/0411267 with Ricardo Schiappa Oxford, February 2009 Outline What exactly
More informationOn Special Geometry of Generalized G Structures and Flux Compactifications. Hu Sen, USTC. Hangzhou-Zhengzhou, 2007
On Special Geometry of Generalized G Structures and Flux Compactifications Hu Sen, USTC Hangzhou-Zhengzhou, 2007 1 Dreams of A. Einstein: Unifications of interacting forces of nature 1920 s known forces:
More informationGRAVITY DUALS OF 2D SUSY GAUGE THEORIES
GRAVITY DUALS OF 2D SUSY GAUGE THEORIES BASED ON: 0909.3106 with E. Conde and A.V. Ramallo (Santiago de Compostela) [See also 0810.1053 with C. Núñez, P. Merlatti and A.V. Ramallo] Daniel Areán Milos,
More informationConstrained BF theory as gravity
Constrained BF theory as gravity (Remigiusz Durka) XXIX Max Born Symposium (June 2010) 1 / 23 Content of the talk 1 MacDowell-Mansouri gravity 2 BF theory reformulation 3 Supergravity 4 Canonical analysis
More informationCharged Spinning Black Holes & Aspects Kerr/CFT Correspondence
Charged Spinning Black Holes & Aspects Kerr/CFT Correspondence I. Black Holes in Supergravities w/ Maximal Supersymmetry (Review) Asymptotically Minkowski (ungauged SG) & anti-desitter space-time (gauged
More informationEinstein 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
More informationTrapped 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,
More informationOne Step Forward and One Step Back (In Understanding Quantum Black Holes) Gary Horowitz UC Santa Barbara
One Step Forward and One Step Back (In Understanding Quantum Black Holes) Gary Horowitz UC Santa Barbara Commun. Math. Phys. 88, 295-308 (1983) Communications in Mathematical Physics Springer-Verlag 1983
More informationarxiv:gr-qc/ v2 1 Oct 1998
Action and entropy of black holes in spacetimes with cosmological constant Rong-Gen Cai Center for Theoretical Physics, Seoul National University, Seoul, 151-742, Korea Jeong-Young Ji and Kwang-Sup Soh
More informationCharged, Rotating Black Holes in Higher Dimensions
Brigham Young University BYU ScholarsArchive All Theses and Dissertations -7-3 Charged, Rotating Black Holes in Higher Dimensions Christopher Bruce Verhaaren Brigham Young University - Provo Follow this
More informationThree-Charge Supertubes in a Rotating Black Hole Background
Three-Charge Supertubes in a Rotating Black Hole Background http://arxiv.org/abs/hep-th/0612085 Eastern Gravity Meeting The Pennsylvania State University Tehani Finch Howard University Dept. of Physics
More informationBlack-hole & white-hole horizons for capillary-gravity waves in superfluids
Black-hole & white-hole horizons for capillary-gravity waves in superfluids G. Volovik Helsinki University of Technology & Landau Institute Cosmology COSLAB Particle Particle physics Condensed matter Warwick
More informationA5682: Introduction to Cosmology Course Notes. 2. General Relativity
2. General Relativity Reading: Chapter 3 (sections 3.1 and 3.2) Special Relativity Postulates of theory: 1. There is no state of absolute rest. 2. The speed of light in vacuum is constant, independent
More informationEinstein 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
More informationLate-time tails of self-gravitating waves
Late-time tails of self-gravitating waves (non-rigorous quantitative analysis) Piotr Bizoń Jagiellonian University, Kraków Based on joint work with Tadek Chmaj and Andrzej Rostworowski Outline: Motivation
More informationA 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
More informationGeneral Relativity and Differential
Lecture Series on... General Relativity and Differential Geometry CHAD A. MIDDLETON Department of Physics Rhodes College November 1, 2005 OUTLINE Distance in 3D Euclidean Space Distance in 4D Minkowski
More informationBlack holes, black strings and cosmological constant. 418-th WE-Heraeus Seminar, Bremen, August 2008
Black holes, black strings and cosmological constant Yves Brihaye Université de Mons-Hainaut Mons, BELGIUM 418-th WE-Heraeus Seminar, Bremen, 25-29 August 2008 Outline of the talk Introduction. The models
More informationThe Role of Black Holes in the AdS/CFT Correspondence
The Role of Black Holes in the AdS/CFT Correspondence Mario Flory 23.07.2013 Mario Flory BHs in AdS/CFT 1 / 30 GR and BHs Part I: General Relativity and Black Holes Einstein Field Equations Lightcones
More informationNon-Abelian Einstein-Born-Infeld Black Holes
Non-Abelian Einstein-Born-Infeld Black Holes arxiv:hep-th/0004130v1 18 Apr 2000 Marion Wirschins, Abha Sood and Jutta Kunz Fachbereich Physik, Universität Oldenburg, Postfach 2503 D-26111 Oldenburg, Germany
More informationParticle Dynamics Around a Charged Black Hole
Particle Dynamics Around a Charged Black Hole Sharif, M. and Iftikhar, S. Speaker: Sehrish Iftikhar Lahore College for Women University, Lahore, Pakistan Layout of the Talk Basic Concepts Dynamics of Neutral
More informationGeneral Relativity and the Black Ring Coordinate System
General Relativity and the Black Ring Coordinate System Daniel Wertheimer Supervisor: Prof. K Zoubos January 2, 2017 1 Contents 1 Introduction 2 1.1 Background Knowledge.......................... 2 1.2
More informationAccelerating 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
More informationarxiv:gr-qc/ v1 26 Aug 1997
Action and entropy of lukewarm black holes SNUTP 97-119 Rong-Gen Cai Center for Theoretical Physics, Seoul National University, Seoul, 151-742, Korea arxiv:gr-qc/9708062v1 26 Aug 1997 Jeong-Young Ji and
More informationStability of black holes and solitons in AdS. Sitter space-time
Stability of black holes and solitons in Anti-de Sitter space-time UFES Vitória, Brasil & Jacobs University Bremen, Germany 24 Janeiro 2014 Funding and Collaborations Research Training Group Graduiertenkolleg
More informationBlack hole thermodynamics
Black hole thermodynamics Daniel Grumiller Institute for Theoretical Physics Vienna University of Technology Spring workshop/kosmologietag, Bielefeld, May 2014 with R. McNees and J. Salzer: 1402.5127 Main
More informationNewman-Penrose formalism in higher dimensions
Newman-Penrose formalism in higher dimensions V. Pravda various parts in collaboration with: A. Coley, R. Milson, M. Ortaggio and A. Pravdová Introduction - algebraic classification in four dimensions
More informationBlack holes with only one Killing field
Black holes with only one Killing field Óscar J. C. Dias a, Gary T. Horowitz b, Jorge E. Santos b a DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA,
More informationThe Uses of Ricci Flow. Matthew Headrick Stanford University
The Uses of Ricci Flow Matthew Headrick Stanford University String theory enjoys a rich interplay between 2-dimensional quantum field theory gravity and geometry The most direct connection is through two-dimensional
More informationBlack rings with a small electric charge: gyromagnetic ratios and algebraic alignment
Published by Institute of Physics Publishing for SISSA Received: September 18, 2006 Accepted: November 16, 2006 Published: December 18, 2006 Black rings with a small electric charge: gyromagnetic ratios
More informationSome Comments on Kerr/CFT
Some Comments on Kerr/CFT and beyond Finn Larsen Michigan Center for Theoretical Physics Penn State University, September 10, 2010 Outline The Big Picture: extremal limit of general black holes. Microscopics
More informationTO GET SCHWARZSCHILD BLACKHOLE SOLUTION USING MATHEMATICA FOR COMPULSORY COURSE WORK PAPER PHY 601
TO GET SCHWARZSCHILD BLACKHOLE SOLUTION USING MATHEMATICA FOR COMPULSORY COURSE WORK PAPER PHY 601 PRESENTED BY: DEOBRAT SINGH RESEARCH SCHOLAR DEPARTMENT OF PHYSICS AND ASTROPHYSICS UNIVERSITY OF DELHI
More informationBlack holes in the 1/D expansion
Black holes in the 1/D expansion Roberto Emparan ICREA & UBarcelona w/ Tetsuya Shiromizu, Ryotaku Suzuki, Kentaro Tanabe, Takahiro Tanaka R μν = 0 R μν = Λg μν Black holes are very important objects in
More informationMicroscopic entropy of the charged BTZ black hole
Microscopic entropy of the charged BTZ black hole Mariano Cadoni 1, Maurizio Melis 1 and Mohammad R. Setare 2 1 Dipartimento di Fisica, Università di Cagliari and INFN, Sezione di Cagliari arxiv:0710.3009v1
More informationBlack Hole Entropy and Gauge/Gravity Duality
Tatsuma Nishioka (Kyoto,IPMU) based on PRD 77:064005,2008 with T. Azeyanagi and T. Takayanagi JHEP 0904:019,2009 with T. Hartman, K. Murata and A. Strominger JHEP 0905:077,2009 with G. Compere and K. Murata
More informationElectromagnetic Energy for a Charged Kerr Black Hole. in a Uniform Magnetic Field. Abstract
Electromagnetic Energy for a Charged Kerr Black Hole in a Uniform Magnetic Field Li-Xin Li Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 (December 12, 1999) arxiv:astro-ph/0001494v1
More informationHolography Duality (8.821/8.871) Fall 2014 Assignment 2
Holography Duality (8.821/8.871) Fall 2014 Assignment 2 Sept. 27, 2014 Due Thursday, Oct. 9, 2014 Please remember to put your name at the top of your paper. Note: The four laws of black hole mechanics
More informationHeterotic Torsional Backgrounds, from Supergravity to CFT
Heterotic Torsional Backgrounds, from Supergravity to CFT IAP, Université Pierre et Marie Curie Eurostrings@Madrid, June 2010 L.Carlevaro, D.I. and M. Petropoulos, arxiv:0812.3391 L.Carlevaro and D.I.,
More informationGeometric inequalities for black holes
Geometric inequalities for black holes Sergio Dain FaMAF-Universidad Nacional de Córdoba, CONICET, Argentina. 3 August, 2012 Einstein equations (vacuum) The spacetime is a four dimensional manifold M with
More informationClassification 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
More informationClassical and thermodynamic stability of black holes
Classical and thermodynamic stability of black holes Ricardo Jorge Ferreira Monteiro Dissertation submitted for the Degree of Doctor of Philosophy at the University of Cambridge Department of Applied Mathematics
More informationFourth Aegean Summer School: Black Holes Mytilene, Island of Lesvos September 18, 2007
Fourth Aegean Summer School: Black Holes Mytilene, Island of Lesvos September 18, 2007 Central extensions in flat spacetimes Duality & Thermodynamics of BH dyons New classical central extension in asymptotically
More informationBlack Holes and Wave Mechanics
Black Holes and Wave Mechanics Dr. Sam R. Dolan University College Dublin Ireland Matematicos de la Relatividad General Course Content 1. Introduction General Relativity basics Schwarzschild s solution
More informationTheory. V H Satheeshkumar. XXVII Texas Symposium, Dallas, TX December 8 13, 2013
Department of Physics Baylor University Waco, TX 76798-7316, based on my paper with J Greenwald, J Lenells and A Wang Phys. Rev. D 88 (2013) 024044 with XXVII Texas Symposium, Dallas, TX December 8 13,
More informationInterpolating geometries, fivebranes and the Klebanov-Strassler theory
Interpolating geometries, fivebranes and the Klebanov-Strassler theory Dario Martelli King s College, London Based on: [Maldacena,DM] JHEP 1001:104,2010, [Gaillard,DM,Núñez,Papadimitriou] to appear Universitá
More informationAnalytic Kerr Solution for Puncture Evolution
Analytic Kerr Solution for Puncture Evolution Jon Allen Maximal slicing of a spacetime with a single Kerr black hole is analyzed. It is shown that for all spin parameters, a limiting hypersurface forms
More information