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 $500$km/s in the case of spinning configurations, and have lead to predictions of a maximum kick of up to $1300$km/s. We test these predictions and demonstrate that kick velocities of at least $2500$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