Relativity at the Age of Gravitational WaveDetection
Fethi M RamazanogluPrinceton University
0 1000 2000 3000
-0.002
-0.001
0
0.001
0.002
Re(r M Ψ4 ) l=2, m=2
3800 3900 4000
-0.06
-0.03
0
0.03
0.06
(tS-r*)/M (t
S-r*)/M
Middle East Technical UniversityAnkara
July 8, 2013
Fethi M Ramazanoglu Numerical Relativity
Outline of talk
A brief introduction to General Relativity
Gravitational wavesSourcesDetection
Numerical RelativityWhy numerical methods?Challenges
Astrophysical numerical relativity
Numerical Relativity beyond astrophysics
Conclusions and questions
Fethi M Ramazanoglu Numerical Relativity
General Relativity
Currently established theory of spacetime and gravitation(Einstein 1916). “Gravity” is simply due to curvature inspacetime. Distances in spacetime are measured by the metricds2 = gabdxadxb.
Einstein equations couplespacetime curvature to theenergy-momentum of matter:
Gab = 8π Tab,
where Gab is a tensorcontaining (up to) 2nd
derivatives of gab
Fethi M Ramazanoglu Numerical Relativity
Gravitational Waves
Ripples in spacetime, produced by changing quadrupolemoment of energy. Analoguous to EM waves generated bycharge dipoles.gab = gBG
ab + hab
Very hard to produce
P = −325
G4
c5(m1m2)
2(m1+m2))r5
Sun-earth system∼ 200W . Tiny!BHB mergers P ∼ M−2.Huge! But 1/r2 kills it!∆`/` ∼ 10−21
Fethi M Ramazanoglu Numerical Relativity
Gravitational Waves
Gravitational Waves are already observed.
Hulse-Taylor Binary (PSRB1913+16)Only indirectlyOnly weak field regime
Fethi M Ramazanoglu Numerical Relativity
Gravitational Waves: Sources
Solar mass: Binary Black Holes (BBH), Binary NeutronStars (NSNS), BHNSSo far, mostly quasi-circular, recently eccentric as wellSupermassive Black Hole Binaries (galaxy mergers)Extreme Mass Ratio Inspirals (EMRIs)White Dwarf Binaries..Big bang...???
0 1000 2000 3000
-0.002
-0.001
0
0.001
0.002
Re(r M Ψ4 ) l=2, m=2
3800 3900 4000
-0.06
-0.03
0
0.03
0.06
(tS-r*)/M (t
S-r*)/M
Fethi M Ramazanoglu Numerical Relativity
Gravitational Waves: Sources
Fethi M Ramazanoglu Numerical Relativity
Gravitational Waves: Detection
LIGO, Virgo: Solar mass (kHz). Ground based.Operational in 2016LISA: SMBH mergers, EMRIs. Space based(0.01− 100 mHz)Pulsar timing arrays: SMBH mergers (nHz). CurrentlyoperationalCMB observatories: B-modes in polarization
New possible sources: Eccentric mergers.Fethi M Ramazanoglu Numerical Relativity
Gravitational Waves: Detection
New possible sources: Eccentric mergers.Fethi M Ramazanoglu Numerical Relativity
Gravitational Waves: Detection
Source systems not very well understood.
Nlow (yr−1) Nre(yr−1) Nhigh(yr−1)
NS-NS 0.4 40 400NS-BH 0.2 10 300BH-BH 0.4 20 1000
New possible sources: Eccentric mergers.
Fethi M Ramazanoglu Numerical Relativity
Pulsar Timing Arrays
Fethi M Ramazanoglu Numerical Relativity
Numerical Relativity
Enstein equations are a mix of elliptic and hyperbolic equations.
3+1 decomposition:space+timeHyperbolic piece: Timeevolution2gab = lower derivativesPick initial data andevolve
Fethi M Ramazanoglu Numerical Relativity
Why Numerical Relativity?
Simply no other (known) way in the strong field regime!
r/M >> 1: Post Newtonian Theory. Breaks down at smallr (breaks down in worse ways as well)After merger: Black hole perturbation theoryNear the merger: Numerical Relativity
Contributes most to the LIGO signalLeads to surprising discoveries
Critical collapse (Choptuik, 1993)Turbulent instability of AdS spacetime (Bizon andRostworowski, 2011)
0 1000 2000 3000
-0.002
-0.001
0
0.001
0.002
Re(r M Ψ4 ) l=2, m=2
3800 3900 4000
-0.06
-0.03
0
0.03
0.06
(tS-r*)/M (t
S-r*)/M
Fethi M Ramazanoglu Numerical Relativity
Numerical Relativity: A pit of snakes
Hyperbolicity is not manifest: Pick the right coordinates(BSSN 1995,1998, Pretorius 2005)Avoid coordinate singularities: Again, pick the rightcoordinates.Handle (time evolving) physical singularities: Movingpunctures, excision.Control constraint violation: Constraint damping.Generate accurate and physical initial data: Ellipticalsolvers, more.Wildly different length scales: Adaptive mesh refinement(AMR)High computational cost: Parallel programming
Fethi M Ramazanoglu Numerical Relativity
AMR, Constraint Violation
2Ai + DiDjAj = Di∂t Φ
C = DiEi , ∂tC = 0
Γ = DiAi
∂t Γ = −DiEi − DiDiΦ + a2C
0 =(∂2
t + a2DiDi)
C
Fethi M Ramazanoglu Numerical Relativity
Numerical Relativity: First Holy Grail
Fethi M Ramazanoglu Numerical Relativity
Astrophysical Simulations
Quasi-circular NS-NS
Fethi M Ramazanoglu Numerical Relativity
Astrophysical Simulations
Eccentric NS-NS
Fethi M Ramazanoglu Numerical Relativity
Astrophysical Simulations
BBH Harizon merger
Fethi M Ramazanoglu Numerical Relativity
Astrophysical Simulations
Test gravity in the strong field.Direct detection of GWs.Learn about compact object populations.Constrain nuclear equation of stateExplain high energy EM phenomena: GRBs and moreUnderstand nucleosynthesis (R process)
Fethi M Ramazanoglu Numerical Relativity
Coincident detection
EM waves and GWs atthe same time.Localization, triggeringUnderstanding GRBsElucidate the nature ofnew transients
Fethi M Ramazanoglu Numerical Relativity
Future directions: More physics, more astrophysics
Realistic NS EOSEM: Forcefree→ Ideal MHD→ Resistive MHDRealistic NS structureNeutrinos: Leakage→ Transport. . .
Fethi M Ramazanoglu Numerical Relativity
Testing GR: Spontaneous Scalarization
Damour, Esposito-Farese, PRL 1993
S =1
16πG
∫d4x√−g
[R − 2gab ∂aφ∂bφ
]+ SM(A2(φ)gab, ψ) A(φ) = e−β/2 φ2
gab≡ A2(φ)gab
Fethi M Ramazanoglu Numerical Relativity
Why Spontaneous?
Novak, PRD 1998
Fethi M Ramazanoglu Numerical Relativity
Parameter Range
Novak, PRD 1998
−15.0 −13.0 −11.0 −9.0 −7.0 −5.0 −3.0
β0
0.0
0.4
0.8
1.2
1.6
2.0
MB [M
so
l]
Polytrope γ=2.34
Spontaneous ScalarizationSpontaneous Scalarization
unstable configurations
Fethi M Ramazanoglu Numerical Relativity
Matter Density
Fethi M Ramazanoglu Numerical Relativity
Scalar field
Fethi M Ramazanoglu Numerical Relativity
Gravitational Waves
200 250 300 350 400 450
−5
0
5
x 10−4
time (Mirr
)
C2
2M
irr
noST
ST
Fethi M Ramazanoglu Numerical Relativity
Comeback times
E/M T (ms)noST 0.0083 7.5
ST 0.0134 3.8
Fethi M Ramazanoglu Numerical Relativity
Beyond Astrophysics
Critical collapseHigher dimensional gravityAdS/CFTQuantum Gravity/CosmologyMathematical relativity
Fethi M Ramazanoglu Numerical Relativity
Information Loss
Fix background metric, look at quantumfields (Hawking ’74-’75):
Blacks holes radiate energyRadiation is thermal
Solution:Full Quantum Gravity?Semiclassical terms? Still hard in3 + 1 = 4D
⇒ 1 + 1 = 2D
Fethi M Ramazanoglu Numerical Relativity
Some Peculiarities of 2D
More null infinities.Conformal flatness:gab = Ω−1ηab
Dimensionless G~
I+R
I−R
I+L
I−L
z− z+
EventHorizon
singularity
collapsingmatter
Fethi M Ramazanoglu Numerical Relativity
Unitarity in 2D (a la ATV)
Fethi M Ramazanoglu Numerical Relativity
Unitarity vs Information Loss
Unitarity is saved, but some information is lost?
−25 −20 −15 −10 −5 00
0.5
1
1.5
y−
sh
F*
M*=14 w=0
M*=12 w=0
M*=9.5 w=1
M*=6 w=0
M*=6 w=0.25
M*=6 w=0.5
M*=6 w=1
I+R
I−R
I+L
I−L
z− z+
singularity last ray
dynamicalhorizon
collapsingmatter
Fethi M Ramazanoglu Numerical Relativity
AdS/CFT Correspondence
Arguably hottest topic in string theory circlesQuantum gravity on AdS5 bulk↔ SSYM theory on theboundaryPossible insights to QCD, CMT(?)Contact with experiment with RHIC (?)
Fethi M Ramazanoglu Numerical Relativity
Dynamical Superradiance
Extract energy froma rotating black holeProvenperturbatively(Teukolsky, Press1974)Never examined instrong, dynamicalsettings.
Fethi M Ramazanoglu Numerical Relativity
Conclusions
LIGO is funded, operational by the end of the decade. NRessential for data analysis.Detection→ GW astronomy including coincident searches.Probing strong field gravity for the first time.Beyond astrophysics, connections to QG, particle physics,more?Possibly a second golden age for relativity.
Fethi M Ramazanoglu Numerical Relativity