In this paper, we examine the efficiency of gravitational bremsstrahlung production in the process of head-on collision of two boosted Schwarzschild black holes. We construct initial data for the characteristic initial value problem in Robinson-Trautman space-times, which represent two instantaneously stationary Schwarzschild black holes in motion toward each other with the same velocity. The Robinson-Trautman equation is integrated for these initial data using a numerical code based on the Galerkin method. The resulting final configuration is a boosted black hole with Bondi mass greater than the sum of the individual masses of the individual initial black holes. Two relevant aspects of the process are presented. The first relates the efficiency ∆ of the energy extraction by gravitational wave emission to the mass of the final black hole. This relation is fitted by a 2049 Int. J. Mod. Phys. D 2008.17:2049-2064. Downloaded from www.worldscientific.com by PURDUE UNIVERSITY on 04/12/15. For personal use only. 2050 R. F. Aranha et al.distribution function of nonextensive thermostatistics with entropic parameter q 1/2; the result extends and validates analysis based on the linearized theory of gravitational wave emission. The second aspect 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.
We examine numerically the post-merger regime of two nonspining holes in non-head-on collisions in the realm of nonaxisymmetric Robinson-Trautman spacetimes. Characteristic initial data for the system are constructed and evolved via the Robinson-Trautman equation. The numerical integration is performed using a Galerkin spectral method which is sufficiently stable to reach the final configuration of the remnant black hole, when the gravitational wave emission ceases. The initial data contains three independent parameters, the ratio mass of the individual colliding black holes, their initial premerger infalling velocity and the incidence angle of collision 0 . The remnant black hole is characterized by its final boost parameter, rest mass and scattering angle. The motion of the remnant black hole is restricted to the plane determined by the directions of the two initial colliding black holes, characterizing a planar collision. The net momentum fluxes carried out by gravitational waves are confined to this plane. We evaluate the efficiency of mass-energy extraction, the total energy and momentum carried out by gravitational waves and the momentum distribution of the remnant black hole for a large domain of initial data parameters. Our analysis is based on the Bondi-Sachs four-momentum conservation laws. The process of mass-energy extraction is shown to be less efficient as the initial data departs from the head-on configuration. Head-on collisions ( 0 ¼ 0 o ) and orthogonal collisions ( 0 ¼ 90 ) constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extraction. On the contrary, head-on collisions and orthogonal collisions constitute, respectively, lower and upper bounds for the momentum of the remnant. Distinct regimes of gravitational wave emission (bursts or quiescent emission) are characterized by the analysis of the time behavior of the gravitational wave power as a function of . In particular, the net gravitational wave flux is nonzero for equal-mass colliding black holes in non-head-on collisions. The momentum extraction and the patterns of the momentum fluxes, as a function of the incidence angle, are examined. The relation between the incidence angle and the scattering angle closely approximates a relation for the inelastic collision of classical particles in Newtonian dynamics.
We examine the phase space dynamics of closed Friedmann-Robertson-Walker universes with a massive inflaton field, where the Friedmann equations contain additional terms arising from high energy corrections to cosmological scenarios. The model is based upon a Randall-Sundrum type of action, with an extra timelike dimension, and the corrections implement nonsingular bounces in the early evolution of the universe. In narrow windows of the parameter space of the models non-linear resonance phenomena of Kolmogorov-Arnold-Moser tori are shown to occur, leading to the destruction of tori that trap the inflaton. As a consequence the escape into inflation takes place. These resonance windows are labeled with an integer n ≥ 2, where n is related to the ratio of the frequencies in the scale factor to those in the scalar field degrees of freedom. We examine the constraints imposed by non-linear resonance in the physical domain of parameters of the model so that inflation may be realized. The larger the order n of the resonance, the stronger the gravitational interaction in the braneworld universe inflated from initial conditions connected with the resonance considered. We also discuss the structural stability of the resonance pattern, the complex dynamics arising in this pre-inflationary phase and some of its possible imprints in the physics of inflation.
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