Black-hole dynamicsin extensions of general relativity

Helvi Witek

Theoretical Particle Physics and CosmologyDepartment of Physics,King’s College London

European Einstein Toolkit Workshop, IST Lisbon, 13 September 2018

H. Witek (KCL) 1 / 15

Why go beyond our standard models?

Gravity• Is general relativity correct?

• Where is it valid?

Cosmology• What is dark matter?

High-energy physics• Quantum gravity?

• Test general relativity in new regimes• Extensions of general relativity

• Beyond-standard model particle physics

⇒ Gravitational waves as search engines for new physics

H. Witek (KCL) 2 / 15

A new observational window: gravitational waves

Groundbased detectors

Laser Interferometer Gravitational wave Observatory – Livingston

Spacebased detectors

Laser Interferometer Space Antenna – artistic impression

• sources: stellar-mass black holes,neutron stars, . . .

• sources: massive black holes,extreme mass-ratio inspirals, . . .

2015 2020s 2030s

LIGO

1st detection

LIGO/Virgo

KAGRA

LIGO India Einstein Telescope

Cosmic Explorer

LISA pathfinder LISA Decigo

Pulsar timing arrays

H. Witek (KCL) 3 / 15

A need for theoretical predictions

• gravitational wave detections are theory-driven

• waveform templates needed for identification and interpretation of signal

• so far: (almost) only in GR, i.e., we are deaf to any “non-vanilla” models!

700 600 500 400 300 200 100 0 100 200(t tmerger rex)/M

0.10

0.05

0.00

0.05

0.10

r ex

4,22

Inspiral

post-Newtonian/effective-one-bodysome extensions known

Merger

NumericalRelativityscarce!

?Ringdown

perturbationtheory

(credit: Witek '18)

Gravitational wave signal of a black hole binary

H. Witek (KCL) 4 / 15

State-of-the-art in NumRel beyond GR

-6x10-5

-4x10-5

-2x10-5

0

2x10-5

4x10-5

6x10-5

8x10-5

0.0001

0 200 400 600 800 1000

r ex Ψ

4,2

2

(t - rex) / M0

(a/M)0 = 0.90(a/M)0 = 0.95

(Witek & Zilhao, in prep.)

Black holes and light fundamental fields(Witek et al ’12; Okawa, Witek, Cardoso ’14; Zilhao, Witek, Cardoso ’15; East ’17, ’18 )

• formation of scalar/vector condensates dueto superradiant instability

• monochromatic gravitational radiation

⇒ search for beyond standard model particles

NOTE: thorns publicly available

• in Canuda (https://bitbucket.org/canuda/)

• soon in Einstein Toolkit (under revision by P. Diener, E. Schnetter & ETK Maintainer team)

see also:

• compact binaries in scalar-tensor theory (Barausse et al ’12, Shibata et al ’13, Healy et al ’11, Berti et al ’13 )

• boson stars (Liebling & Palenzuela ’12, Palenzuela et al ’17, Helfer et al ’18, . . . ), Proca stars (Sanchis-Gual et al ’18)

• Einstein-Maxwell-Dilaton models (Hirschmann et al ’17)

• dynamical Chern-Simons gravity (Okounkova et al ’17)

H. Witek (KCL) 5 / 15

Here:

Einstein-dilaton Gauss-Bonnetgravity

(in prep. with L. Gualtieri, P. Pani, T. Sotiriou)

action in quadratic gravity (e.g. Kanti et al ’95, Alexander & Yunes ’09, Yunes & Siemens ’13, . . . )

S =1

16π

∫d4x√−g(

(4)R + 2αGBf (Φ)RGB + αCSh(Ψ) ∗R R − 1

2(∇Φ)2

)

Gab =1

2TΦab − αGBGGB

ab ,

Φ =− 2αGBf′(Φ)RGB

• RGB = R2 − 4RabRab + RabcdR

abcd

• typically: f (Φ) ∼ eΦ

1 21see Okounkova et al ’17 for parity violating (dynamical Chern-Simons) sector2use geometric units c = 1 = G

H. Witek (KCL) 6 / 15

Why EdGB gravity?

High-energy physics

• higher curvature correctionsrelevant in strong-curvature regime

• low-energy limit of some string theories(Gross & Sloan ’87, Kanti et al ’95, Moura & Schiappa 06)

• compactification of Lovelock gravity(Charmousis ’14)

• representative for more involved theories

H. Witek (KCL) 7 / 15

Black holes in EdGB

• black holes have scalar hair (of the second kind)!(Kanti et al ’95, Pani et al ’09, ’11, Stein et al ’11, Sotiriou & Zhou ’14, Ayzenberg & Yunes ’14, Maselli et al ’15, . . . )

• black holes can exceed the Kerr bound (Kleihaus et al ’11, ’14)

• signatures in black hole binaries:• scalar dipole radiation⇒ shift in binding energy⇒ shift in orbital frequency

• ringdown signature?• effects in nonlinear regime?

Constraints on coupling

• regular BH horizons & lightest observed BHs M ∼ 5M:√|αGB| . 7km

• x-ray binary A0620-00 :√|αGB| . 10km (Yagi ’12)

• inspiral of GW151226 :√|αGB| . 27km (Yagi, Yunes & Pretorius ’16)

H. Witek (KCL) 8 / 15

EdGB as effective field theory

Mathematical considerations:

• recall: well-posed initial value formulation necessary for numerical stability

• field equations are second order ⇒ potential for well-posed PDE system?• in a generalized harmonic gauge only weakly hyperbolic (Papallo & Reall ’17, Papallo ’17)

• good chances as effective field theory (Choquet-Bruhat ’88, Delsate, Hilditch & Witek ’14)

• expansion gab = g(0)ab + εg

(1)ab +O(ε2), Φ = Φ(0) + εΦ(1) +O(ε2)

• ε 1 and αGB/M2 ∼ O(ε)

• note: vacuum, i.e., Tab = Tab(Φ)

ε0 : G(0)ab =

1

2T

(0)ab , (0)Φ(0) = 0 ⇒ (g

(0)ab ,Φ

(0)) = (gGRab , 0)

ε1 : G(1)ab = 0 , (0)Φ(1) = −f ′R(0)

GB ⇒ (g(1)ab ,Φ

(1)) = (0,Φ(1))3

3Note: drop superscript in the following and remember gab ≡ gGRab , Φ ≡ Φ(1)

H. Witek (KCL) 9 / 15

Numerical implementation

• EFT approach up to O(ε)⇒ evolve scalar field & GR background simultaneously

• implemented in Einstein Toolkit & Canuda(https://bitbucket.org/canuda/) einsteintoolkit.org

GR code – ETK & Canuda

ADMBasedefines metric gfs

TwoPuncturesmetric initial data

McLachlan or Canuda-Leanmetric evolution

AHFinderDirect,WeylScal4 or Canuda-NPScalars

Multipole

EdGB code – Canuda

EdGB Basedefines scalar gfs

EdGB Initscalar field initial data

EdGB Evolscalar field evolution

H. Witek (KCL) 10 / 15

Numerical simulations in EdGB

Setup

• ε(0): non-spinning BH binary with d/M = 10 and mass-ratiosq = m1/m2 = 1, 1/2, 1/4

• ε(1): zero initial scalar field or superposition of solutions

Scalar field evolution

H. Witek (KCL) 11 / 15

Scalar radiation

measured at rex/M = 100

q = 1

0.5

0.0

0.5

r ex

22

NRPN 10 4

10 2

100

0.05

0.00

0.05

r ex

44

NRPN

10 4

10 2

800 600 400 200 0t/M

0.05

0.00

0.05

r ex

4,22

4, 22

50 0 50 100t/M

10 6

10 4

10 2

q = 1/2

101

r ex

11

10 3

100

0.50.00.5

r ex

22

10 3

100

0.20.00.2

r ex

33

10 3

100

0.1

0.0

0.1

r ex

44

10 3

100

800 600 400 200 0t/M

0.050.000.05

r ex

4,22

0 50 100t/M

10 6

10 3

• early inspiral: agreement with PN prediction (Yagi et al ’11)

• modulated ringdown (frequency domain so far only for Schwarzschild!)

• superposition of scalar-led and gravitational-led modes• quality factors different for pure Kerr and Kerr + GWs

H. Witek (KCL) 12 / 15

Validity of EFT approach

estimate second order effects: G(2)ab = 1

2Teffab

(g

(0)ab ,Φ

(1))

Instantaneous validity

• compare energy fluxes

• |εInst| .√

2 EGW

E (2)

Secular effects

• compare phase evolution

• |εSec| .√

2φ(0)(t)φ(2)(t)

with φ(k) =∫dtΩ(k)

800 700 600 500 400 300 200 100 0(t tmerger)/M

10 2

10 1

100

||

Inst, q = 1sec, q = 1

Inst, q = 1/2sec, q = 1/2

Inst, q = 1/4sec, q = 1/4

H. Witek (KCL) 13 / 15

Observational constraints

non-detection of dephasing ⇒ bound on GB coupling: |ε| = |αGB

4M2 | .√

∆φdet

φ(2)

104

105

|GB

| [km

] M = 105MLISA, q = 1LISA, q = 1/2LISA, q = 1/4

800 700 600 500 400 300 200 100 0(t tmerger)/M

100

101

102

|GB

| [km

] M = 20M LIGO, q = 1LIGO, q = 1/2LIGO, q = 1/4

3G, q = 13G, q = 1/23G, q = 1/4

• e.g.: GW151226-type system: αGB,LIGO . 2.7km αGB,3G . 1.5km

⇒ 2− 4 times better than exisiting constraints

• bounds improve for smaller-mass systems & smaller mass ratio

H. Witek (KCL) 14 / 15

Take home message• GWs as new observational channel for beyond-standard model physics

• BUT: limited by our lack of knowledge of the merger phase in beyond-GR⇒ need novel analytic & numerical methods to model waveforms

• interested?consider joining the Einstein Toolkit group “Cosmology and particles”

• here: first binary black hole evolutions in EdGB• numerical infrastructure available in Canuda• most stringent observational bounds so far• improvement for 3G detections (smaller mass with higher SNR)

• next steps to connect theories with observations⇒ more detailed analysis and comparison with observations⇒ complete waveforms (PN+NR+perturbations)⇒ actual searches or novel constraints

Thank you!

acknowledgements:

H. Witek (KCL) 15 / 15