Article

# Binary black hole coalescence in the large-mass-ratio limit: the hyperboloidal layer method and waveforms at null infinity

07/2011; DOI:10.1103/PhysRevD.84.084026
Source: arXiv

ABSTRACT We compute and analyze the gravitational waveform emitted to future null
infinity by a system of two black holes in the large mass ratio limit. We
consider the transition from the quasi-adiabatic inspiral to plunge, merger,
and ringdown. The relative dynamics is driven by a leading order in the mass
ratio, 5PN-resummed, effective-one-body (EOB), analytic radiation reaction. To
compute the waveforms we solve the Regge-Wheeler-Zerilli equations in the
time-domain on a spacelike foliation which coincides with the standard
Schwarzschild foliation in the region including the motion of the small black
hole, and is globally hyperboloidal, allowing us to include future null
infinity in the computational domain by compactification. This method is called
the hyperboloidal layer method, and is discussed here for the first time in a
study of the gravitational radiation emitted by black hole binaries. We
consider binaries characterized by five mass ratios, $\nu=10^{-2,-3,-4,-5,-6}$,
that are primary targets of space-based or third-generation gravitational wave
detectors. We show significative phase differences between finite-radius and
null-infinity waveforms. We test, in our context, the reliability of the
extrapolation procedure routinely applied to numerical relativity waveforms. We
present an updated calculation of the gravitational recoil imparted to the
merger remnant by the gravitational wave emission. As a self consistency test
of the method, we show an excellent fractional agreement (even during the
plunge) between the 5PN EOB-resummed mechanical angular momentum loss and the
gravitational wave angular momentum flux computed at null infinity. New results
concerning the radiation emitted from unstable circular orbits are also
presented.

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2 Nov 2012

### Keywords

black holes

computational domain

excellent fractional agreement

extrapolation procedure

gravitational recoil imparted

gravitational wave emission

gravitational waveform

hyperboloidal layer method

large mass ratio limit

mass ratios

numerical relativity waveforms

Regge-Wheeler-Zerilli equations

self consistency test

significative phase differences

time-domain

unstable circular orbits

updated calculation