Probing strong-field gravity Black holes and mergers in general relativity and beyond Leo C. Stein (TAPIR, Caltech) January 23, 2018 — CaJAGWR seminar
Preface Me, Kent Yagi, Nico Yunes Maria (Masha) Okounkova Baoyi Chen Many other colleagues, SXS collaboration, taxpayers Leo C. Stein (Caltech) Probing strong-field gravity 1
Probing strong-field gravity Black holes and mergers in general relativity and beyond Leo C. Stein (TAPIR, Caltech) January 23, 2018 — CaJAGWR seminar Leo C. Stein (Caltech) Probing strong-field gravity 2
Knowns and unknowns Leo C. Stein (Caltech) Probing strong-field gravity 3
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. . . Leo C. Stein (Caltech) Probing strong-field gravity 4
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. . . • Neutron stars • GRB relation, central engine, r-process elements. . . • Dense nuclear equation of state? Leo C. Stein (Caltech) Probing strong-field gravity 4
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. . . • Neutron stars • GRB relation, central engine, r-process elements. . . • Dense nuclear equation of state? • Testing general relativity Leo C. Stein (Caltech) Probing strong-field gravity 4
Why test GR? General relativity successful but incomplete G ab = 8 π ˆ T ab • Can’t have mix of quantum/classical • GR not renormalizable • GR+QM=new physics (e.g. BH information paradox) Leo C. Stein (Caltech) Probing strong-field gravity 5
Why test GR? General relativity successful but incomplete G ab = 8 π ˆ T 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, . . . • Deeper understanding of breakdown, quantum regime of GR • Need to explore strong-field Leo C. Stein (Caltech) Probing strong-field gravity 5
Study black holes • BH thermodynamics = ⇒ breakdown • GR+QM both important Leo C. Stein (Caltech) Probing strong-field gravity 6
Study black holes • Nonrotating black holes: lots of symmetry, easy to study • Rotating BHs: not enough symmetry; rely on (complicated) Teukolsky • Near-horizon extremal Kerr simple again! • Bonus: T → 0 , most quantum black holes • Recently showed Teukolsky not needed in NHEK Chen + LCS, PRD 96 , 064017 (2017) [arXiv:1707.05319] [Bardeen, Press, Teukolsky (1972)] • Kerr/CFT: are black holes a critical point? Leo C. Stein (Caltech) Probing strong-field gravity 7
Why test GR? General relativity successful but incomplete G ab = 8 π ˆ T 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) Probing strong-field gravity 8
[Baker, Psaltis, Skordis (2015)] -10 10 NS -14 10 BH -18 10 R -22 WD 10 MS Satellite -26 PSRs 10 BBN -2 ) -30 MW SMBH Curvature, ξ (cm 10 -34 10 S stars M87 -38 SS 10 M -42 10 -46 Last scattering 10 CMB peaks -50 10 Galaxies Clusters -54 10 Lambda -58 Accn. 10 P(k)| z=0 scale -62 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 10 Potential, ε
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) Probing strong-field gravity 10
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 , 024010 (2016) [arXiv:1510.02152] Leo C. Stein (Caltech) Probing strong-field gravity 11
x y t t=0 t=T n C r,T Identify 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 , 024010 (2016) [arXiv:1510.02152] Leo C. Stein (Caltech) Probing strong-field gravity 11
Distant compact binaries Parameterize over multipole moments: LCS, Yagi PRD 89 , 044026 (2014) [arXiv:1310.6743] 10 0 1 Ξ� � Gm � r 3 � 1 � 2 � km � 1 � � inv. curvature radius � NS � � � timing 10 2 � Ω NS merger � 0.001 � BH merger dCS 10 4 � � km � 10 � 6 10 6 SMBH merger Earth's � EDGB surface J0737 10 8 � � � 3039 � 10 � 9 � LAGEOS Sun's 10 10 surface Mercury LLR precession � � 10 � 12 10 � 12 10 � 10 10 � 8 10 � 6 10 � 4 0.01 1 � � Gm � r � compactness � Leo C. Stein (Caltech) Probing strong-field gravity 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) Probing strong-field gravity 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) Probing strong-field gravity 13
How to perform precision tests • Two approaches: theory-specific and theory-agnostic • Agnostic: parameterize, e.g. PPN, PPE Leo C. Stein (Caltech) Probing strong-field gravity 14
Parameterized post-Einstein framework • Insert power-law corrections to amplitude and phase ( u 3 ≡ π M f ) ˜ 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) Probing strong-field gravity 15
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) Probing strong-field gravity 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 Problem: Only simulated BBH mergers in GR!* Leo C. Stein (Caltech) Probing strong-field gravity 16
The problem From Lehner+Pretorius 2014: Don’t know if other theories have good initial value problem Leo C. Stein (Caltech) Probing strong-field gravity 17
Numerical relativity Leo C. Stein (Caltech) Probing strong-field gravity 18
Numerical relativity • Nonlinear, quasilinear, 2nd order hyperbolic PDE, 10 functions, 3+1 coordinates • Attempts from ’60s until 2005. 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) Probing strong-field gravity 19
Numerical relativity • Nonlinear, quasilinear, 2nd order hyperbolic PDE, 10 functions, 3+1 coordinates • Attempts from ’60s until 2005. 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) Probing strong-field gravity 19
Some other theories “Scalar-tensor”: � ∂ µ ϕ∂ ν ϕ − 1 � − 1 G ⋆ 2 g ⋆ µν ∂ σ ϕ∂ σ ϕ 2 g ⋆ µν V ( ϕ ) + 8 πT ⋆ µν = 2 µν ✷ g ⋆ ϕ = − 4 πα ( 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) Probing strong-field gravity 20
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