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
