Relativity at the Age of Gravitational Wave Detection€¦ · Relativity at the Age of Gravitational Wave Detection Fethi M Ramazanoglu˘ Princeton University 0 1000 2000 3000-0.002-0.001

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


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


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


Gravitational Waves

Gravitational Waves are already observed.

Hulse-Taylor Binary (PSRB1913+16)Only indirectlyOnly weak field regime


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


Gravitational Waves: Sources


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


New possible sources: Eccentric mergers.Fethi M Ramazanoglu Numerical Relativity


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.


Pulsar Timing Arrays


Numerical Relativity

Enstein equations are a mix of elliptic and hyperbolic equations.

3+1 decomposition:space+timeHyperbolic piece: Timeevolution2gab = lower derivativesPick initial data andevolve


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


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


AMR, Constraint Violation

2Ai + DiDjAj = Di∂t Φ

C = DiEi , ∂tC = 0

Γ = DiAi

∂t Γ = −DiEi − DiDiΦ + a2C

0 =(∂2

t + a2DiDi)

C


Numerical Relativity: First Holy Grail


Astrophysical Simulations

Quasi-circular NS-NS



Eccentric NS-NS



BBH Harizon merger



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)


Coincident detection

EM waves and GWs atthe same time.Localization, triggeringUnderstanding GRBsElucidate the nature ofnew transients


Future directions: More physics, more astrophysics

Realistic NS EOSEM: Forcefree→ Ideal MHD→ Resistive MHDRealistic NS structureNeutrinos: Leakage→ Transport. . .


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


Why Spontaneous?

Novak, PRD 1998


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


Matter Density


Scalar field


Gravitational Waves

200 250 300 350 400 450

−5

0

5

x 10−4

time (Mirr

)

C2

2M

irr

noST

ST


Comeback times

E/M T (ms)noST 0.0083 7.5

ST 0.0134 3.8


Beyond Astrophysics

Critical collapseHigher dimensional gravityAdS/CFTQuantum Gravity/CosmologyMathematical 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


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


Unitarity in 2D (a la ATV)


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


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 (?)


Dynamical Superradiance

Extract energy froma rotating black holeProvenperturbatively(Teukolsky, Press1974)Never examined instrong, dynamicalsettings.


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.


Documents

Relativity at the Age of Gravitational Wave Detection€¦ · Relativity at the Age of Gravitational Wave Detection Fethi M Ramazanoglu˘ Princeton University 0 1000 2000 3000-0.002-0.001