74 research outputs found
Pair of null gravitating shells III. Algebra of Dirac's observables
The study of the two-shell system started in ``Pair of null gravitating
shells I and II'' (gr-qc/0112060--061) is continued. The pull back of the
Liouville form to the constraint surface, which contains complete information
about the Poisson brackets of Dirac observables, is computed in the singular
double-null Eddington-Finkelstein (DNEF) gauge. The resulting formula shows
that the variables conjugate to the Schwarzschild masses of the intershell
spacetimes are simple combinations of the values of the DNEF coordinates on
these spacetimes at the shells. The formula is valid for any number of in- and
out-going shells. After applying it to the two-shell system, the symplectic
form is calculated for each component of the physical phase space; regular
coordinates are found, defining it as a symplectic manifold. The symplectic
transformation between the initial and final values of observables for the
shell-crossing case is written down.Comment: 26 pages, Latex file using amstex, some references correcte
Resonant recoil in extreme mass ratio binary black hole mergers
The inspiral and merger of a binary black hole system generally leads to an
asymmetric distribution of emitted radiation, and hence a recoil of the remnant
black hole directed opposite to the net linear momentum radiated. The recoil
velocity is generally largest for comparable mass black holes and particular
spin configurations, and approaches zero in the extreme mass ratio limit. It is
generally believed that for extreme mass ratios eta<<1, the scaling of the
recoil velocity is V {\propto} eta^2, where the proportionality coefficient
depends on the spin of the larger hole and the geometry of the system (e.g.
orbital inclination). Here we show that for low but nonzero inclination
prograde orbits and very rapidly spinning large holes (spin parameter
a*>0.9678) the inspiralling binary can pass through resonances where the
orbit-averaged radiation-reaction force is nonzero. These resonance crossings
lead to a new contribution to the kick, V {\propto} eta^{3/2}. For these
configurations and sufficiently extreme mass ratios, this resonant recoil is
dominant. While it seems doubtful that the resonant recoil will be
astrophysically significant, its existence suggests caution when extrapolating
the results of numerical kick results to extreme mass ratios and near-maximal
spins.Comment: fixed references; matches PRD accepted version (minor revision); 9
pages, 2 figure
Black-hole binary simulations: the mass ratio 10:1
We present the first numerical simulations of an initially non-spinning
black-hole binary with mass ratio as large as 10:1 in full general relativity.
The binary completes approximately 3 orbits prior to merger and radiates about
0.415% of the total energy and 12.48% of the initial angular momentum in the
form of gravitational waves. The single black hole resulting from the merger
acquires a kick of about 66.7 km/s relative to the original center of mass
frame. The resulting gravitational waveforms are used to validate existing
formulas for the recoil, final spin and radiated energy over a wider range of
the symmetric mass ratio parameter eta=M1*M2/(M1+M2)^2 than previously
possible. The contributions of l > 2 multipoles are found to visibly influence
the gravitational wave signal obtained at fixed inclination angles.Comment: To match published versio
The effect of gravitational-wave recoil on the demography of massive black holes
The coalescence of massive black hole (MBH) binaries following galaxy mergers
is one of the main sources of low-frequency gravitational radiation. A
higher-order relativistic phenomenon, the recoil as a result of the non-zero
net linear momentum carried away by gravitational waves, may have interesting
consequences for the demography of MBHs at the centers of galaxies. We study
the dynamics of recoiling MBHs and its observational consequences. The
``gravitational rocket'' may: i) deplete MBHs from late-type spirals, dwarf
galaxies, and stellar clusters; ii) produce off-nuclear quasars, including
unusual radio morphologies during the recoil of a radio-loud source; and iii)
give rise to a population of interstellar and intergalactic MBHs.Comment: emulateapj, 5 pages, 2 figures, to appear in the ApJ Letter
Maximum gravitational recoil
Recent calculations of gravitational radiation recoil generated during
black-hole binary mergers have reopened the possibility that a merged binary
can be ejected even from the nucleus of a massive host galaxy. Here we report
the first systematic study of gravitational recoil of equal-mass binaries with
equal, but anti-aligned, spins parallel to the orbital plane. Such an
orientation of the spins is expected to maximize the recoil. We find that
recoil velocity (which is perpendicular to the orbital plane) varies
sinusoidally with the angle that the initial spin directions make with the
initial linear momenta of each hole and scales up to a maximum of ~4000 km/s
for maximally-rotating holes. Our results show that the amplitude of the recoil
velocity can depend sensitively on spin orientations of the black holes prior
to merger.Comment: 4 pages, 4 figs, revtex
Modeling gravitational recoil from precessing highly-spinning unequal-mass black-hole binaries
We measure the gravitational recoil for unequal-mass-black- hole-binary
mergers, with the larger BH having spin a/m^H=0.8, and the smaller BH
non-spinning. We choose our configurations such that, initially, the spins lie
on the orbital plane. The spin and orbital plane precess significantly, and we
find that the out-of plane recoil (i.e. the recoil perpendicular to the orbital
plane around merger) varies as \eta^2 / (1+q), in agreement with our previous
prediction, based on the post-Newtonian scaling.Comment: Published version. 15 pages, 11 figures, revtex
Comparison of Numerical and Post-Newtonian Waveforms for Generic Precessing Black-Hole Binaries
We compare waveforms and orbital dynamics from the first long-term, fully
non-linear, numerical simulations of a generic black-hole binary configuration
with post-Newtonian predictions. The binary has mass ratio q~0.8 with
arbitrarily oriented spins of magnitude S_1/m_1^2~0.6 and S_2/m_2^2~0.4 and
orbits 9 times prior to merger. The numerical simulation starts with an initial
separation of r~11M, with orbital parameters determined by initial 2.5PN and
3.5PN post-Newtonian evolutions of a quasi-circular binary with an initial
separation of r=50M. The resulting binaries have very little eccentricity
according to the 2.5PN and 3.5PN systems, but show significant eccentricities
of e~0.01-0.02 and e~0.002-0.005 in the respective numerical simulations, thus
demonstrating that 3.5PN significantly reduces the eccentricity of the binary
compared to 2.5PN. We perform three numerical evolutions from r~11M with
maximum resolutions of h=M/48,M/53.3,M/59.3, to verify numerical convergence.
We observe a reasonably good agreement between the PN and numerical waveforms,
with an overlap of nearly 99% for the first six cycles of the (l=2,m=+-2)
modes, 91% for the (l=2,m=+-1) modes, and nearly 91% for the (l=3,m=+-3) modes.
The phase differences between numerical and post-Newtonian approximations
appear to be independent of the (l,m) modes considered and relatively small for
the first 3-4 orbits. An advantage of the 3.5 PN model over the 2.5 PN one
seems to be observed, which indicates that still higher PN order (perhaps even
4.0PN) may yield significantly better waveforms. In addition, we identify
features in the waveforms likely related to precession and precession-induced
eccentricity.Comment: New figures, enhanced analysis, revisions throughout the pape
Supermassive recoil velocities for binary black-hole mergers with antialigned spins
Recent calculations of the recoil velocity in binary black hole mergers have
found the kick velocity to be of the order of a few hundred km/s in the case of
non-spinning binaries and about km/s in the case of spinning
configurations, and have lead to predictions of a maximum kick of up to km/s. We test these predictions and demonstrate that kick velocities of at
least km/s are possible for equal-mass binaries with anti-aligned spins
in the orbital plane. Kicks of that magnitude are likely to have significant
repercussions for models of black-hole formation, the population of
intergalactic black holes and the structure of host galaxies.Comment: Final version, published by Phys. Rev. Lett.; title changed according
to suggestion of PRL; note added after preparation of manuscrip
- …