Numerical black hole mergers beyond general relativity

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1 Numerical black hole mergers beyond general relativity Leo C. Stein (Theoretical Caltech) YKIS2018a

2 Preface Me, Kent Yagi, Nico Yunes Takahiro Tanaka Maria (Masha) Okounkova Many other colleagues, SXS collaboration, taxpayers

3 Numerical black hole mergers beyond general relativity Leo C. Stein (Theoretical Caltech) YKIS2018a

4 Goal: Use gravitational waves for precision tests of general relativity (and beyond) in the dynamical, non-linear, strong field Leo C. Stein (Caltech) Numerical BH mergers beyond GR 1

5 Goal: Use gravitational waves for precision tests of general relativity (and beyond) in the dynamical, non-linear, strong field General relativity must be incomplete LIGO: New opportunity to test GR in strong-field Present tests shortcomings Almost no theory-specific tests Theory-independent tests need more guidance Challenge: Find spacetime solutions in theories beyond GR Our contribution: First binary black hole mergers in dynamical Chern-Simons gravity General method appropriate for many deformations of GR Still lots of work to do, stay tuned or get involved! Leo C. Stein (Caltech) Numerical BH mergers beyond GR 1

6 Knowns and unknowns Gravitational waves are here to stay. Get as much science out as possible Binary black hole populations Mass function, spins, clusters/fields, progenitors, evolution... Testing general relativity Neutron stars GRB relation, central engine, r-process elements... Dense nuclear equation of state? Leo C. Stein (Caltech) Numerical BH mergers beyond GR 2

7 Why test GR? General relativity successful but incomplete G ab = 8π ˆT ab Can t have mix of quantum/classical GR not renormalizable GR+QM=new physics (e.g. BH information paradox) Leo C. Stein (Caltech) Numerical BH mergers beyond GR 3

8 Why test GR? General relativity successful but incomplete G ab = 8π ˆT ab Can t have mix of quantum/classical GR not renormalizable GR+QM=new physics (e.g. BH information paradox) Approach #1: Theory Look for good UV completion = strings, loops,... Need to explore strong-field Deeper understanding of breakdown, quantum regime of GR Leo C. Stein (Caltech) Numerical BH mergers beyond GR 4

9 Why test GR? General relativity successful but incomplete G ab = 8π ˆT ab Can t have mix of quantum/classical GR not renormalizable GR+QM=new physics (e.g. BH information paradox) Approach #2: Empiricism Ultimate test of theory: ask nature So far, only precision tests are weak-field Lots of theories GR Need to explore strong-field Strong curvature non-linear dynamical Leo C. Stein (Caltech) Numerical BH mergers beyond GR 5

10 [Baker, Psaltis, Skordis (2015)] Curvature, ξ (cm -2 ) BBN M Last scattering Lambda Satellite SS Galaxies WD MS PSRs S stars CMB peaks Clusters P(k) z=0 NS MW SMBH M Potential, ε R BH Accn. scale 10 0

11 Big picture Before aligo: precision tests of GR in weak field Weak field: distant binary of black holes or neutron stars Leo C. Stein (Caltech) Numerical BH mergers beyond GR 7

12 Big picture Before aligo: precision tests of GR in weak field Weak field: distant binary of black holes or neutron stars Now: first direct measurements of dynamical, strong field regime Future: precision tests of GR in the strong field Changing nuclear EOS is degenerate with changing gravity Need black hole binary merger for precision Leo C. Stein (Caltech) Numerical BH mergers beyond GR 8

13 Big picture Before aligo: precision tests of GR in weak field Weak field: distant binary of black holes or neutron stars Now: first direct measurements of dynamical, strong field regime Future: precision tests of GR in the strong field Changing nuclear EOS is degenerate with changing gravity Need black hole binary merger for precision Question: How to perform precision tests of GR in strong field? Leo C. Stein (Caltech) Numerical BH mergers beyond GR 8

14 How to perform precision tests Two approaches: theory-specific and theory-agnostic Agnostic: parameterize, e.g. PPN, PPE Leo C. Stein (Caltech) Numerical BH mergers beyond GR 9

15 Parameterized post-einstein framework Insert power-law corrections to amplitude and phase (u 3 πmf) h(f) = h GR (f) (1 + αu a ) exp[iβu b ] Parameters: (α, a, β, b) Inspired by post-newtonian calculations in beyond-gr theories Leo C. Stein (Caltech) Numerical BH mergers beyond GR 10

16 How to perform precision tests Two approaches: theory-specific and theory-agnostic Agnostic: parameterize, e.g. PPN, PPE Want more powerful parameterization Don t know how to parameterize in strong-field! Need guidance from specific theories Leo C. Stein (Caltech) Numerical BH mergers beyond GR 11

17 How to perform precision tests Two approaches: theory-specific and theory-agnostic Agnostic: parameterize, e.g. PPN, PPE Want more powerful parameterization Don t know how to parameterize in strong-field! Need guidance from specific theories Problem: Only simulated BBH mergers in GR!* Leo C. Stein (Caltech) Numerical BH mergers beyond GR 11

18 The problem From Lehner+Pretorius 2014: Don t know if other theories have good initial value problem Leo C. Stein (Caltech) Numerical BH mergers beyond GR 12

19 Numerical relativity Nonlinear, quasilinear, 2nd order hyperbolic PDE, 10 functions, 3+1 coordinates Attempts from 60s until Merging BHs for 13 years Want to evolve. How do you know if good IBVP? Both under- and over-constrained. gauge constraints (not all data free; need constraint damping) Avoid singularities: punctures or excision Leo C. Stein (Caltech) Numerical BH mergers beyond GR 13

20 Numerical relativity Nonlinear, quasilinear, 2nd order hyperbolic PDE, 10 functions, 3+1 coordinates Attempts from 60s until Merging BHs for 13 years Want to evolve. How do you know if good IBVP? Both under- and over-constrained. gauge constraints (not all data free; need constraint damping) Avoid singularities: punctures or excision Every other gravity theory will have at least these difficulties Leo C. Stein (Caltech) Numerical BH mergers beyond GR 13

21 Some other theories Scalar-tensor : G µν = 2 ( µ ϕ ν ϕ 1 ) 2 g µν σ ϕ σ ϕ 1 2 g µνv (ϕ) + 8πTµν g ϕ = 4πα(ϕ)T + 1 dv 4 dϕ BBH in S-T: Massless scalar = ϕ 0, agrees with GR Only differ if funny boundary or initial conditions Hirschmann+ paper on Einstein-Maxwell-dilaton Leo C. Stein (Caltech) Numerical BH mergers beyond GR 14

22 Some other theories Higher derivative EOMs Ostrogradski instability. H unbounded below Some theories try to avoid, e.g. Horndeski Massive gravity theories. B-D ghost, cured by drgt. Problems even with second-derivative EOMs: If not quasi-linear, may have ( t φ) 2 Source, but... Papallo and Reall papers on Lovelock, Horndeski, EdGB Leo C. Stein (Caltech) Numerical BH mergers beyond GR 15

23 A solution Leo C. Stein (Caltech) Numerical BH mergers beyond GR 16

24 A solution Treat every theory as an effective field theory (EFT) Particle and condensed matter physicists always do this. Sorta do this for GR. Valid below some scale Theory only needs to be approximate, approximately well-posed General relativity Standard Model QED h 0 Maxwell G 0 Special relativity v/c 0 post-newtonian Example: weak force below EWSB scale (lose unitarity above) Leo C. Stein (Caltech) Numerical BH mergers beyond GR 17

25 A solution Treat every theory as an effective field theory (EFT) Particle and condensed matter physicists always do this. Sorta do this for GR. Valid below some scale Theory only needs to be approximate, approximately well-posed General relativity Standard Model QED h 0 Maxwell G 0 Special relativity v/c 0 post-newtonian Example: weak force below EWSB scale (lose unitarity above) Leo C. Stein (Caltech) Numerical BH mergers beyond GR 17

26 A solution General relativity Standard Model QED h 0 Maxwell G 0 Special relativity v/c 0 post-newtonian Same should happen in gravity EFT: lose predictivity (bad initial value problem) above some scale Theory valid below cutoff Λ E. Must recover GR for Λ. Assume weak coupling, use perturbation theory Leo C. Stein (Caltech) Numerical BH mergers beyond GR 18

27 A solution General relativity Standard Model QED h 0 Maxwell G 0 Special relativity v/c 0 post-newtonian Same should happen in gravity EFT: lose predictivity (bad initial value problem) above some scale Theory valid below cutoff Λ E. Must recover GR for Λ. Assume weak coupling, use perturbation theory Example: Dynamical Chern-Simons gravity Leo C. Stein (Caltech) Numerical BH mergers beyond GR 18

28 What is dynamical Chern-Simons gravity? Chern-Simons = GR + axion + interaction S = d 4 x [ g R 1 ] 2 ( ϑ)2 + ε ϑ RR ϑ = ε RR, G ab + ε C ab [ ϑ 3 g] = T ab Anomaly cancellation, low-e string theory, LQG... (see Nico s review Phys. Rept. 480 (2009) 1-55) Lowest-order EFT with parity-odd ϑ, shift symmetry (long range) Phenomenology unique from other R 2 (e.g. Einstein-dilaton-Gauss-Bonnet) Gravity version of QCD axion, sourced by rotation Leo C. Stein (Caltech) Numerical BH mergers beyond GR 19

29 Black holes in dcs a = 0 (Schwarzschild) is exact solution with ϑ = 0 Rotating BHs have dipole+ scalar hair LCS, PRD 90, (2014) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 20

30 Black holes in dcs a = 0 (Schwarzschild) is exact solution with ϑ = 0 Rotating BHs have dipole+ scalar hair LCS, PRD 90, (2014) [arxiv: ] Extremal: QCG 33, (2016) [arxiv: ] Coming soon, NHEK (with Baoyi Chen) Post-Newtonian of BBH inspiral in PRD (2012) [arxiv: ] See also review CQG (2015) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 20

31 Back to problem and solution DCS had principal part 3 g coming from C ab tensor. Probably not well-posed, Delsate/Hilditch/Witek PRD 91, Theory is GR + ε deformation. Expand everything in ε Derivation At every order in ε, principal part is Princ[G ab ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 21

32 Back to problem and solution DCS had principal part 3 g coming from C ab tensor. Probably not well-posed, Delsate/Hilditch/Witek PRD 91, Theory is GR + ε deformation. Expand everything in ε Derivation At every order in ε, principal part is Princ[G ab ] Background dynamics are well-posed = perturbations well-posed Leo C. Stein (Caltech) Numerical BH mergers beyond GR 21

33 Leo C. Stein (Caltech) Numerical BH mergers beyond GR 22

34 From Okounkova, LCS+, PRD 96, (2017) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 22 Mode amplitude 6 (GM)Re[RΨ (2,2) 4 ] (l/gm) 2 Re[Rϑ (1) (1,0) ] Numerical Post-Newtonian (l/gm) 2 Re[Rϑ (1) (2,1) ] 10 3 (l/gm) 2 Re[Rϑ (1) (3,2) ] (t t Peak )/GM 10 2

35 From Okounkova, LCS+, PRD 96, (2017) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR Ė (0) NR (l/gm) 4 Ė (ϑ,2) NR (l/gm) 4 Ė (ϑ,2) PN Ė (GM) ẑ 0.3ẑ 0.1ẑ 0.0ẑ (t t Peak )/GM 10 3

36 Instantaneous regime of validity l/gm ẑ 0.1ẑ 0.0ẑ Perturbation theory invalid Perturbation theory valid (t t Merger )/GM 10 3 From Okounkova, LCS+, PRD 96, (2017) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 23

37 Secular regime of validity dephasing LIGO most sensitive to phase Expand phase in ε around time t 0 φ = φ (0) + ε 2 φ + O(ε 3 ), φ(t) = φ(t 0 ) + (t t 0 ) d φ dt t=t (t t 0) 2 d2 φ dt 2 t=t0 + O(t t 0 ) 3 Pretend orbits quasicircular, adiabatic = E = E(ω(t)) Use chain rule, relate d ω/dt to energy, flux Leo C. Stein (Caltech) Numerical BH mergers beyond GR 24

38 Secular regime of validity dephasing (l/gm) 4 φ ẑ 0.1ẑ 0.0ẑ (GM)Re[RΨ (2,2) 4 ] χ 1,2 = 0.3ẑ (t t 0 )/GM 10 2 From Okounkova, LCS+, PRD 96, (2017) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 25

39 Bounds φ gw = 2 φ σ φ Spin M bound M 60M ( l ( GM l ( GM l GM ) ( σφ ) 1/ l 11 km ( σ φ ) ( σφ ) 1/ l 18 km ( σ φ 0.1 ) 1.4 ( σφ 0.1) 1/4 ) 1/4 0.1) 1/4 7 orders of magnitude improvement over Solar System Leo C. Stein (Caltech) Numerical BH mergers beyond GR 26

40 Future work Lots of work to do! Work in progress on O(ε 2 ) Run lots of simulations Waveform modeling: build surrogates! > > > import NRSur7dq2 Study degeneracy Bayesian model selection with existing LIGO/Virgo detections Turn the crank: explore more theories Guide theory-agnostic parameterizations Leo C. Stein (Caltech) Numerical BH mergers beyond GR 27

41 First binary black hole mergers in dcs Inspiral: qualitative agreement with analytics Merger: discovered new phenomenology, dipole burst Estimated φ, bound on l O(10) km For better bounds: Higher SNR Longer waveform/lower mass Higher BH spins Working on O(ε 2 ) For details, see Okounkova, LCS+, PRD 96, (2017) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 28

Goal: Use gravitational waves for precision tests of general relativity (and beyond) in the dynamical, non-linear, strong field General relativity must be incomplete LIGO: New opportunity to test GR

42 Goal: Use gravitational waves for precision tests of general relativity (and beyond) in the dynamical, non-linear, strong field General relativity must be incomplete LIGO: New opportunity to test GR in strong-field Present tests shortcomings Almost no theory-specific tests Theory-independent tests need more guidance Challenge: Find spacetime solutions in theories beyond GR Our contribution: First binary black hole mergers in dynamical Chern-Simons gravity General method appropriate for many deformations of GR Still lots of work to do, stay tuned or get involved! Leo C. Stein (Caltech) Numerical BH mergers beyond GR 29

43 Other slides Leo C. Stein (Caltech) Numerical BH mergers beyond GR 30

Distant compact binaries Post-Newtonian: bodies are point particles Motion of distant bodies boils down to multipoles Different theories, different moments ( hairs ) Brans-Dicke: NS,

44 Distant compact binaries Post-Newtonian: bodies are point particles Motion of distant bodies boils down to multipoles Different theories, different moments ( hairs ) Brans-Dicke: NS, BH EDGB: NS, BH DCS: dipoles... BH proof by Sotiriou, Zhou NS proof by Yagi, LCS, Yunes PRD 93, (2016) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 31

45 Distant compact binaries Identify t C r,t t=t n Post-Newtonian: bodies are point particles Motion of distant bodies boils down to multipoles Different theories, different moments ( hairs ) Brans-Dicke: NS, BH EDGB: NS, BH DCS: dipoles... x y t=0 BH proof by Sotiriou, Zhou NS proof by Yagi, LCS, Yunes PRD 93, (2016) [arxiv: ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 31

46 Distant compact binaries Parameterize over multipole moments: LCS, Yagi PRD 89, (2014) [arxiv: ] Ξ Gm r km 1 inv. curvature radius LLR Earth's surface LAGEOS Mercury precession dcs EDGB Sun's surface Ω timing J NS NS merger BH merger SMBH merger ε km Leo C. Stein (Caltech) Numerical BH mergers beyond GR 32

47 Next issues Gravitational waves at O(ε 2 ): Two sets of gauges, constraints Find stable gauge Linearization of damped harmonic But may experience secular drift (hint: Kerr PT ) Regime of validity of perturbation scheme ε 2 h (2) g (0) Renormalization? See e.g. Galley and Rothstein [ ] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 33

Only 10 numbers in parametrized post-newtonian [Slide from Wex] Metric:' PPN formalism for metric theories of gravity g 00 = 1+2U 2 U 2 2 W +(2 +2+ 3 + 1 2 ) 1 +2(3 2 +1+ 2 + ) 2 +2(1 + 3) 3 +2(3 +3

48 Only 10 numbers in parametrized post-newtonian [Slide from Wex] Metric:' PPN formalism for metric theories of gravity g 00 = 1+2U 2 U 2 2 W +( ) 1 +2( ) 2 +2(1 + 3) 3 +2( ) 4 ( 1 2 )A ( 1 2 3)w 2 U 2w i w j U ij +(2 3 1)w i V i + O( 3 ), g 0i = 1 2 ( )Vi 1 2 ( )Wi 1 2 ( 1 2 2)wi U 2w j U ij + O( 5/2 ), g ij =(1+2 U) ij + O( 2 ). Z w:"mopon"w.r.t."preferred"reference"frame Z Z Z Z Metric'poten+als:' Z U = 0 x x 0 d3 x 0, Z 0 (x x 0 )i(x x 0 )j Uij = d 3 x 0, x x 0 3 Z 0 00 (x x 0 ) x 0 x 00 W = x x 0 3 x x 00 Z 0 [v 0 (x x 0 )] 2 A = d 3 x 0, x x 0 3 Z Norbert Wex / 2016-Jul-19 / Caltech (Newtonian"potenPal) x x 00 d 3 x 0 d 3 x 00, x 0 x 00 Z Z 1 = Z 2 = Z 3 = 0 v 02 x x 0 d3 x 0, 0 U 0 x x 0 d3 x 0, 0 0 x x 0 d3 x 0, Z Z Vi = 0 vi 0 x x 0 d3 x 0, WMAP/NASA Z 0 [v 0 (x x 0 )](x x 0 )i Wi = d 3 x 0. x x 0 3 Z p 0 4 = x x 0 d3 x 0, Z 0 0 ["Will"1993,"Will&2014,&Living&Reviews&in&Rela9vity&] Leo C. Stein (Caltech) Numerical BH mergers beyond GR 34 8

49 LIGO s tests Leo C. Stein (Caltech) Numerical BH mergers beyond GR 35

50 LIGO s tests Two tests I like: Any deviation from GR must be below 4% of signal power Test of dispersion relation Leo C. Stein (Caltech) Numerical BH mergers beyond GR 36

Binary black hole mergers in Dynamical Chern-Simons gravity

Binary black hole mergers in Dynamical Chern-Simons gravity Leo C. Stein (TAPIR, Caltech) with Maria Okounkova (TAPIR, Caltech) GR21@Columbia 2016 July 12 ( A3) Vision Before this year: precision tests