Second order perturbations of a Schwarzschild black hole: inclusion of odd parity perturbations

We consider perturbations of a Schwarzschild black hole that can be of both even and odd parity, keeping terms up to second order in perturbation theory, for the $\ell=2$ axisymmetric case. We develop explicit formulae for the evolution equations and radiated energies and waveforms using the Regge-Wheeler-Zerilli approach. This formulation is useful, for instance, for the treatment in the ``close limit approximation'' of the collision of counterrotating black holes.Comment: 12 pages RevTe

Colliding black holes: how far can the close approximation go?

We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed waveforms and energy. Much more important, second-order results correctly indicate the range of validity of perturbation theory. This use of second-order, to provide ``error bars,'' makes perturbation theory a viable tool for providing benchmarks for numerical relativity in more generic collisions and, in some range of collision parameters, for supplying waveform templates for gravitational wave detection.Comment: 6 pages, RevTeX, 2 figures included with eps

Evolving the Bowen-York initial data for spinning black holes

The Bowen-York initial value data typically used in numerical relativity to represent spinning black hole are not those of a constant-time slice of the Kerr spacetime. If Bowen-York initial data are used for each black hole in a collision, the emitted radiation will be partially due to the ``relaxation'' of the individual holes to Kerr form. We compute this radiation by treating the geometry for a single hole as a perturbation of a Schwarzschild black hole, and by using second order perturbation theory. We discuss the extent to which Bowen-York data can be expected accurately to represent Kerr holes.Comment: 10 pages, RevTeX, 4 figures included with psfi

The Efficiency of Gravitational Bremsstrahlung Production in the Collision of Two Schwarzschild Black Holes

We examine the efficiency of gravitational bremsstrahlung production in the process of head-on collision of two boosted Schwarzschild black holes. We constructed initial data for the characteristic initial value problem in Robinson-Trautman spacetimes, that represent two instantaneously stationary Schwarzschild black holes in motion towards each other with the same velocity. The Robinson-Trautman equation was integrated for these initial data using a numerical code based on the Galerkin method. The final resulting configuration is a boosted black hole with Bondi mass greater than the sum of the individual mass of each initial black hole. Two relevant aspects of the process are presented. The first relates the efficiency $\Delta$ of the energy extraction by gravitational wave emission to the mass of the final black hole. This relation is fitted by a distribution function of non-extensive thermostatistics with entropic parameter $q \simeq 1/2$; the result extends and validates analysis based on the linearized theory of gravitational wave emission. The second is a typical bremsstrahlung angular pattern in the early period of emission at the wave zone, a consequence of the deceleration of the black holes as they coalesce; this pattern evolves to a quadrupole form for later times.Comment: 16 pages, 4 figures, to appear in Int. J. Modern Phys. D (2008

Making use of geometrical invariants in black hole collisions

We consider curvature invariants in the context of black hole collision simulations. In particular, we propose a simple and elegant combination of the Weyl invariants I and J, the {\sl speciality index} ${\cal S}$. In the context of black hole perturbations $\cal S$ provides a measure of the size of the distortions from an ideal Kerr black hole spacetime. Explicit calculations in well-known examples of axisymmetric black hole collisions demonstrate that this quantity may serve as a useful tool for predicting in which cases perturbative dynamics provide an accurate estimate of the radiation waveform and energy. This makes ${\cal S}$ particularly suited to studying the transition from nonlinear to linear dynamics and for invariant interpretation of numerical results.Comment: 4 pages, 3 eps figures, Revte

The collision of boosted black holes: second order close limit calculations

We study the head-on collision of black holes starting from unsymmetrized, Brill--Lindquist type data for black holes with non-vanishing initial linear momentum. Evolution of the initial data is carried out with the ``close limit approximation,'' in which small initial separation and momentum are assumed, and second-order perturbation theory is used. We find agreement that is remarkably good, and that in some ways improves with increasing momentum. This work extends a previous study in which second order perturbation calculations were used for momentarily stationary initial data, and another study in which linearized perturbation theory was used for initially moving holes. In addition to supplying answers about the collisions, the present work has revealed several subtle points about the use of higher order perturbation theory, points that did not arise in the previous studies. These points include issues of normalization, and of comparison with numerical simulations, and will be important to subsequent applications of approximation methods for collisions.Comment: 20 pages, RevTeX, 6 figures included with psfi

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology