Perturbative effects of spinning black holes with applications to recoil velocities

Recently, we proposed an enhancement of the Regge-Wheeler-Zerilli formalism for first-order perturbations about a Schwarzschild background that includes first-order corrections due to the background black-hole spin. Using this formalism, we investigate gravitational wave recoil effects from a spinning black-hole binary system analytically. This allows us to better understand the origin of the large recoils observed in full numerical simulation of spinning black hole binaries.Comment: Proceedings of Theory Meets Data Analysis at Comparable and Extreme Mass Ratios (NRDA/Capra 2010), Perimeter Institute, June 2010 - 12 page

A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit

We obtain a fourth order accurate numerical algorithm to integrate the Zerilli and Regge-Wheeler wave equations, describing perturbations of nonrotating black holes, with source terms due to an orbiting particle. Those source terms contain the Dirac's delta and its first derivative. We also re-derive the source of the Zerilli and Regge-Wheeler equations for more convenient definitions of the waveforms, that allow direct metric reconstruction (in the Regge-Wheeler gauge).Comment: 30 pages, 12 figure

On computations of angular momentum and its flux in numerical relativity

The purpose of this note is to point out ambiguities that appear in the calculation of angular momentum and its radiated counterpart when some simple formulae are used to compute them. We illustrate, in two simple different examples, how incorrect results can be obtained with them. Additionally, we discuss the magnitude of possible errors in well known situations.Comment: 8 pages. Minor improvements . To appear in Class. Quantum Gra

Accurate black hole evolutions by fourth-order numerical relativity

We present techniques for successfully performing numerical relativity simulations of binary black holes with fourth-order accuracy. Our simulations are based on a new coding framework which currently supports higher order finite differencing for the BSSN formulation of Einstein's equations, but which is designed to be readily applicable to a broad class of formulations. We apply our techniques to a standard set of numerical relativity test problems, demonstrating the fourth-order accuracy of the solutions. Finally we apply our approach to binary black hole head-on collisions, calculating the waveforms of gravitational radiation generated and demonstrating significant improvements in waveform accuracy over second-order methods with typically achievable numerical resolution.Comment: 17 pages, 25 figure

Modeling Gravitational Recoil Using Numerical Relativity

We review the developments in modeling gravitational recoil from merging black-hole binaries and introduce a new set of 20 simulations to test our previously proposed empirical formula for the recoil. The configurations are chosen to represent generic binaries with unequal masses and precessing spins. Results of these simulations indicate that the recoil formula is accurate to within a few km/s in the similar mass-ratio regime for the out-of-plane recoil.Comment: corrections to text, 11 pages, 1 figur

Seeking for toroidal event horizons from initially stationary BH configurations

We construct and evolve non-rotating vacuum initial data with a ring singularity, based on a simple extension of the standard Brill-Lindquist multiple black-hole initial data, and search for event horizons with spatial slices that are toroidal when the ring radius is sufficiently large. While evolutions of the ring singularity are not numerically feasible for large radii, we find some evidence, based on configurations of multiple BHs arranged in a ring, that this configuration leads to singular limit where the horizon width has zero size, possibly indicating the presence of a naked singularity, when the radius of the ring is sufficiently large. This is in agreement with previous studies that have found that there is no apparent horizon surrounding the ring singularity when the ring's radius is larger than about twice its mass.Comment: 24 pages, 14 figure

Gravitational-Wave Recoil from the Ringdown Phase of Coalescing Black Hole Binaries

The gravitational recoil or "kick" of a black hole formed from the merger of two orbiting black holes, and caused by the anisotropic emission of gravitational radiation, is an astrophysically important phenomenon. We combine (i) an earlier calculation, using post-Newtonian theory, of the kick velocity accumulated up to the merger of two non-spinning black holes, (ii) a "close-limit approximation" calculation of the radiation emitted during the ringdown phase, and based on a solution of the Regge-Wheeler and Zerilli equations using initial data accurate to second post-Newtonian order. We prove that ringdown radiation produces a significant "anti-kick". Adding the contributions due to inspiral, merger and ringdown phases, our results for the net kick velocity agree with those from numerical relativity to 10-15 percent over a wide range of mass ratios, with a maximum velocity of 180 km/s at a mass ratio of 0.38.Comment: 9 pages, 5 figures; to appear in Class. Quant. Gra

Momentum constraint relaxation

Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint violation and helps improve the quality of the numerical model. We present here a method that controls the violation of the momentum constraint. The method is based on the addition of a longitudinal component to the traceless extrinsic curvature generated by a vector potential w_i, as outlined by York. The components of w_i are relaxed to solve approximately the momentum constraint equations, pushing slowly the evolution toward the space of solutions of the constraint equations. We test this method with simulations of binary neutron stars in circular orbits and show that effectively controls the growth of the aforementioned violations. We also show that a full numerical enforcement of the constraints, as opposed to the gentle correction of the momentum relaxation scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More detailed description of the algorithms are provided. Final published versio

Toward a dynamical shift condition for unequal mass black hole binary simulations

Moving puncture simulations of black hole binaries rely on a specific gauge choice that leads to approximately stationary coordinates near each black hole. Part of the shift condition is a damping parameter, which has to be properly chosen for stable evolutions. However, a constant damping parameter does not account for the difference in mass in unequal mass binaries. We introduce a position dependent shift damping that addresses this problem. Although the coordinates change, the changes in the extracted gravitational waves are small.Comment: 15 pages, submitted to CQG for NRDA 2009 conference proceeding

Comparisons of binary black hole merger waveforms

This a particularly exciting time for gravitational wave physics. Ground-based gravitational wave detectors are now operating at a sensitivity such that gravitational radiation may soon be directly detected, and recently several groups have independently made significant breakthroughs that have finally enabled numerical relativists to solve the Einstein field equations for coalescing black-hole binaries, a key source of gravitational radiation. The numerical relativity community is now in the position to begin providing simulated merger waveforms for use by the data analysis community, and it is therefore very important that we provide ways to validate the results produced by various numerical approaches. Here, we present a simple comparison of the waveforms produced by two very different, but equally successful approaches--the generalized harmonic gauge and the moving puncture methods. We compare waveforms of equal-mass black hole mergers with minimal or vanishing spins. The results show exceptional agreement for the final burst of radiation, with some differences attributable to small spins on the black holes in one case.Comment: Revtex 4, 5 pages. Published versio