Spin-orbit interactions in black-hole binaries

We perform numerical simulations of black-hole binaries to study the exchange of spin and orbital angular momentum during the last, highly nonlinear, stages of the coalescence process. To calculate the transfer of angular momentum from orbital to spin, we start with two quasi-circular configurations, one with initially non-spinning black holes, the other with corotating black holes. In both cases the binaries complete almost two orbits before merging. We find that, during these last orbits, the specific spin (a/m) of each horizon increases by only 0.012 for the initially non-spinning configuration, and by only 0.006 for the initially corotating configuration. By contrast, the corotation value for the specific spin should increase from 0.1 at the initial proper separation of 10M to 0.33 when the proper separation is 5M. Thus the spin-orbit coupling is far too weak to tidally lock the binary to a corotating state during the late-inspiral phase. We also study the converse transfer from spin into orbital motion. In this case, we start the simulations with parallel, highly-spinning non-boosted black holes. As the collision proceeds, the system acquires a non-head-on orbital motion, due to spin-orbit coupling, that leads to the radiation of angular momentum. We are able to accurately measure the energy and angular momentum losses and model their dependence on the initial spins.Comment: This version corrects two typos in Eq (4) and Table I present in the published versio

The last orbit of binary black holes

We have used our new technique for fully numerical evolutions of orbiting black-hole binaries without excision to model the last orbit and merger of an equal-mass black-hole system. We track the trajectories of the individual apparent horizons and find that the binary completed approximately one and a third orbits before forming a common horizon. Upon calculating the complete gravitational radiation waveform, horizon mass, and spin, we find that the binary radiated 3.2% of its mass and 24% of its angular momentum. The early part of the waveform, after a relatively short initial burst of spurious radiation, is oscillatory with increasing amplitude and frequency, as expected from orbital motion. The waveform then transitions to a typical `plunge' waveform; i.e. a rapid rise in amplitude followed by quasinormal ringing. The plunge part of the waveform is remarkably similar to the waveform from the previously studied `ISCO' configuration. We anticipate that the plunge waveform, when starting from quasicircular orbits, has a generic shape that is essentially independent of the initial separation of the binary.Comment: 5 pages, 5 figures, revtex

Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision

We present a new algorithm for evolving orbiting black-hole binaries that does not require excision or a corotating shift. Our algorithm is based on a novel technique to handle the singular puncture conformal factor. This system, based on the BSSN formulation of Einstein's equations, when used with a `pre-collapsed' initial lapse, is non-singular at the start of the evolution, and remains non-singular and stable provided that a good choice is made for the gauge. As a test case, we use this technique to fully evolve orbiting black-hole binaries from near the Innermost Stable Circular Orbit (ISCO) regime. We show fourth order convergence of waveforms and compute the radiated gravitational energy and angular momentum from the plunge. These results are in good agreement with those predicted by the Lazarus approach.Comment: 4 pages, revtex4, 3 figs, references added, typos fixe

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

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

Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen-Press equation. Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us to have access to the gravitational waveform at null infinity in a general setup. We argue that this hyperboloidal approach leads to a more accurate and efficient calculation of the radiation signal than the common approach where a timelike outer boundary is introduced. The method can be generalized to study perturbations of Kerr spacetime using the Teukolsky equation.Comment: 14 pages, 9 figure