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Probing strong-field gravity Black holes and mergers in general - - PowerPoint PPT Presentation

Apr 22, 2023 118 likes •684 views

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

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Probing strong-field gravity

Black holes and mergers in general relativity and beyond Leo C. Stein (TAPIR, Caltech) January 23, 2018 — CaJAGWR seminar

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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

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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

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Knowns and unknowns

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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

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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

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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

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Why test GR?

General relativity successful but incomplete Gab = 8π ˆ Tab

  • Can’t have mix of quantum/classical
  • GR not renormalizable
  • GR+QM=new physics (e.g. BH information paradox)

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Why test GR?

General relativity successful but incomplete Gab = 8π ˆ Tab

  • 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

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Study black holes

  • BH thermodynamics =

⇒ breakdown

  • GR+QM both important

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Study black holes

[Bardeen, Press, Teukolsky (1972)]

  • 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]

  • Kerr/CFT: are black holes

a critical point?

Leo C. Stein (Caltech) Probing strong-field gravity 7

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Why test GR?

General relativity successful but incomplete Gab = 8π ˆ Tab

  • 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

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[Baker, Psaltis, Skordis (2015)]

10

  • 62

10

  • 58

10

  • 54

10

  • 50

10

  • 46

10

  • 42

10

  • 38

10

  • 34

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  • 30

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  • 26

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  • 22

10

  • 18

10

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10

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Curvature, ξ (cm

  • 2)

10

  • 12 10
  • 10 10
  • 8 10
  • 6 10
  • 4 10
  • 2 10

Potential, ε

BBN Lambda Last scattering

WD MS

PSRs

NS

Clusters Galaxies

MW M87 S stars R M SS BH

SMBH P(k)| z=0 Accn. scale Satellite CMB peaks

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Big picture

  • Before aLIGO: precision tests of GR in weak field
  • Weak field: distant binary of black holes or neutron stars

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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

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Distant compact binaries

x y t t=0 t=T n Cr,T Identify

  • 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

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Distant compact binaries

Parameterize over multipole moments: LCS, Yagi PRD 89, 044026 (2014) [arXiv:1310.6743]

  • Sun's

surface Earth's surface LAGEOS J0737 3039 Mercury precession LLR NS merger BH merger SMBH merger NS Ω timing EDGB dCS

1012 1010 108 106 104 0.01 1 1012 109 106 0.001 1 100 102 104 106 108 1010 Gmr compactness ΞGmr312 km1 inv. curvature radius km

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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

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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?

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How to perform precision tests

  • Two approaches: theory-specific and theory-agnostic
  • Agnostic: parameterize, e.g. PPN, PPE

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Parameterized post-Einstein framework

  • Insert power-law corrections to amplitude and phase (u3 ≡ πMf)

˜ h(f) = ˜ hGR(f) × (1 + αua) × exp[iβub]

  • Parameters: (α, a, β, b)
  • Inspired by post-Newtonian calculations in beyond-GR theories

Leo C. Stein (Caltech) Probing strong-field gravity 15

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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

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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!*

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The problem

From Lehner+Pretorius 2014: Don’t know if other theories have good initial value problem

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Numerical relativity

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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

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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

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Some other theories

“Scalar-tensor”: G⋆

µν = 2

  • ∂µϕ∂νϕ − 1

2g⋆

µν∂σϕ∂σϕ

  • − 1

2g⋆

µνV (ϕ) + 8πT ⋆ µν

✷g⋆ϕ = −4πα(ϕ)T ⋆ + 1 4 dV 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

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Some other theories

  • Higher derivative EOMs
  • Ostrogradski instability. H unbounded below
  • Some theories try to avoid, e.g. Horndeski, dRGT
  • Massive gravity theories. B-D ghost, cured by dRGT.
  • Problems even with second-derivative EOMs:

If not quasi-linear, may have (∂tφ)2 ≃ Source, but . . .

  • Papallo and Reall papers on Lovelock, Horndeski, EdGB

(this whole slide )

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A solution

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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 Special relativity post-Newtonian G→0 v/c→0 Standard Model QED Maxwell h→0

  • Example: weak force below EWSB scale (lose unitarity above)

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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 Special relativity post-Newtonian G→0 v/c→0 Standard Model QED Maxwell h→0

  • Example: weak force below EWSB scale (lose unitarity above)

Leo C. Stein (Caltech) Probing strong-field gravity 23

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A solution

General relativity Special relativity post-Newtonian G→0 v/c→0 Standard Model QED Maxwell h→0

  • 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

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A solution

General relativity Special relativity post-Newtonian G→0 v/c→0 Standard Model QED Maxwell h→0

  • 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) Probing strong-field gravity 24

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What is dynamical Chern-Simons gravity?

  • Chern-Simons = GR + axion + interaction

S =

  • d4x√−g
  • R − 1

2(∂ϑ)2 + ε ϑ ∗RR

  • ϑ = ε ∗RR ,

Gab + ε Cab[∂ϑ∂3g] = Tab

  • 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 R2

(e.g. Einstein-dilaton-Gauss-Bonnet)

  • Gravity version of QCD axion, sourced by rotation

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Black holes in dCS

  • a = 0 (Schwarzschild) is exact solution with ϑ = 0
  • Rotating BHs have dipole+ scalar hair

LCS, PRD 90, 044061 (2014) [arXiv:1407.2350]

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Black holes in dCS

  • a = 0 (Schwarzschild) is exact solution with ϑ = 0
  • Rotating BHs have dipole+ scalar hair

LCS, PRD 90, 044061 (2014) [arXiv:1407.2350] Extremal: QCG 33, 235013 (2016) [arXiv:1512.05453] Coming soon, NHEK (with Baoyi Chen)

  • Post-Newtonian of BBH inspiral in

PRD 85 064022 (2012) [arXiv:1110.5950]

  • See also review

CQG 32 243001 (2015) [arXiv:1501.07274]

Leo C. Stein (Caltech) Probing strong-field gravity 26

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Back to problem and solution

  • DCS had principal part ∂3g coming from Cab tensor.

Probably not well-posed, Delsate+ PRD 91, 024027.

  • Theory is GR + ε × deformation. Expand everything in ε
  • Derivation
  • At every order in ε, principal part is Princ[Gab]

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Back to problem and solution

  • DCS had principal part ∂3g coming from Cab tensor.

Probably not well-posed, Delsate+ PRD 91, 024027.

  • Theory is GR + ε × deformation. Expand everything in ε
  • Derivation
  • At every order in ε, principal part is Princ[Gab]

Background dynamics are well-posed = ⇒ perturbations well-posed

Leo C. Stein (Caltech) Probing strong-field gravity 27

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−6 6 ×10−2 (GM)Re[RΨ(2,2)

4

] −2 2 ×10−3 (ℓ/GM)−2Re[Rϑ(1)

(1,0)]

Numerical Post-Newtonian −6 6 ×10−4 (ℓ/GM)−2Re[Rϑ(1)

(2,1)]

−6 −5 −4 −3 −2 −1 1 (t∗ − tPeak)/GM ×102 −1 1 ×10−3 (ℓ/GM)−2Re[Rϑ(1)

(3,2)]

Mode amplitude

From Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

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−3 −2 −1 (t∗ − tPeak)/GM ×103 10−16 10−12 10−8 10−4 ˙ E × (GM)2 0.3ˆ z 0.3ˆ z 0.1ˆ z 0.0ˆ z ˙ E(0) NR (ℓ/GM)−4 ˙ E(ϑ,2) NR (ℓ/GM)−4 ˙ E(ϑ,2) PN From Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

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Next issues

Gravitational waves at O(ε2):

  • 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
  • ε2h(2)
  • ≪
  • g(0)
  • Renormalization? See e.g. Galley and Rothstein [1609.08268]

Leo C. Stein (Caltech) Probing strong-field gravity 29

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Instantaneous regime of validity

0.0 0.2 0.4 0.6 0.8 1.0 1 2 5 10 20 50 aGM GM

Breakdown of perturbation theory Decoupling limit valid From LCS, PRD 90, 044061 (2014) [arXiv:1407.2350]

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Instantaneous regime of validity −2 −1 (t − tMerger)/GM ×103 100 101 |ℓ/GM|

Perturbation theory invalid Perturbation theory valid

0.3ˆ z 0.1ˆ z 0.0ˆ z

From Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

Leo C. Stein (Caltech) Probing strong-field gravity 30

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Secular regime of validity — dephasing

LIGO most sensitive to phase

  • Expand phase in ε around time t0

φ = φ(0) + ε2∆φ + O(ε3) , ∆φ(t) = ∆φ(t0) + (t − t0)d∆φ dt

  • t=t0

+ 1 2(t − t0)2 d2∆φ dt2

  • t=t0 + O(t − t0)3
  • Pretend orbits quasicircular, adiabatic =

⇒ E = E(ω(t))

  • Use chain rule, relate d∆ω/dt to energy, flux

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Secular regime of validity — dephasing

10−7 10−5 10−3 10−1 101 (ℓ/GM)−4∆φ 0.3ˆ z 0.1ˆ z 0.0ˆ z −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 (t∗ − t0)/GM ×102 −3 3 (GM)Re[RΨ(2,2)

4

] ×10−2 χ1,2 = 0.3ˆ z

From Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

Leo C. Stein (Caltech) Probing strong-field gravity 32

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Bounds

∆φgw = 2∆φ σφ Spin M bound M ≈ 60M⊙ 0.3

  • ℓ

GM

  • 0.13

σφ

0.1

1/4 ℓ 11 km σφ

0.1

1/4 0.1

  • ℓ

GM

  • 0.2

σφ

0.1

1/4 ℓ 18 km σφ

0.1

1/4 0.0

  • ℓ

GM

  • 1.4

σφ

0.1

1/4 ✗ — 7 orders of magnitude improvement over Solar System

Leo C. Stein (Caltech) Probing strong-field gravity 33

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Future work

Lots of work to do!

  • Work in progress on O(ε2)
  • 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) Probing strong-field gravity 34

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  • 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(ε2)

For details, see Okounkova, LCS+, PRD 96, 044020 (2017) [arXiv:1705.07924]

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  • General relativity must be incomplete
  • Understand theory better (NHEK work)
  • 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) Probing strong-field gravity 36

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Other slides

Leo C. Stein (Caltech) Probing strong-field gravity 37

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Only 10 numbers in parametrized post-Newtonian [Slide from Wex]

Norbert Wex / 2016-Jul-19 / Caltech

PPN formalism for metric theories of gravity

8

g00 = −1 + 2U − 2βU 2 − 2ξΦW + (2γ + 2 + α3 + ζ1 − 2ξ)Φ1 + 2(3γ − 2β + 1 + ζ2 + ξ)Φ2 +2(1 + ζ3)Φ3 + 2(3γ + 3ζ4 − 2ξ)Φ4 − (ζ1 − 2ξ)A − (α1 − α2 − α3)w2U − α2wiwjUij +(2α3 − α1)wiVi + O(3), g0i = −1 2(4γ + 3 + α1 − α2 + ζ1 − 2ξ)Vi − 1 2(1 + α2 − ζ1 + 2ξ)Wi − 1 2(α1 − 2α2)wiU −α2wjUij + O(5/2), gij = (1 + 2γU)δij + O(2).

U = Z ρ0 |x − x0| d3x0, Uij = Z ρ0(x − x0)i(x − x0)j |x − x0|3 d3x0, ΦW = Z ρ0ρ00(x − x0) |x − x0|3 · x0 − x00 |x − x00| − x − x00 |x0 − x00|

  • d3x0 d3x00,

A = Z ρ0[v0 · (x − x0)]2 |x − x0|3 d3x0, Z Φ1 = Z ρ0v02 |x − x0| d3x0, Φ2 = Z ρ0U 0 |x − x0| d3x0, Φ3 = Z ρ0Π0 |x − x0| d3x0, Φ4 = Z p0 |x − x0| d3x0, Z Z | − | Vi = Z ρ0v0

i

|x − x0| d3x0, Wi = Z ρ0[v0 · (x − x0)](x − x0)i |x − x0|3 d3x0.

Metric'poten+als:' Metric:'

(Newtonian"potenPal)

w:"moPon"w.r.t."preferred"reference"frame

WMAP/NASA

["Will"1993,"Will&2014,&Living&Reviews&in&Rela9vity&] Leo C. Stein (Caltech) Probing strong-field gravity 38

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LIGO’s tests

Leo C. Stein (Caltech) Probing strong-field gravity 39

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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) Probing strong-field gravity 40

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LIGO’s tests

One test I do not particularly like:

  • Insert power-law corrections to amplitude and phase (u3 ≡ πMf)

˜ h(f) = ˜ hGR(f) × (1 + αua) × exp[iβub]

  • Parameters: (α, a, β, b)
  • Inspired by post-Newtonian calculations in beyond-GR theories

Leo C. Stein (Caltech) Probing strong-field gravity 41