The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the finite region of phase space. This critical point engenders in the phase space dynamics the topology of stable and unstable four dimensional tubes R × S 3 , where R is a saddle direction and S 3 is the manifold of unstable periodic orbits in the center-center sector. A general characteristic of the dynamical flow is an oscillatory mode about orbits of an invariant plane of the dynamics which contains the critical point and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of tubes (one stable, one unstable) emerging from the neighborhood of the critical point towards the FRW singularity have homoclinic transversal crossings. The homoclinic intersection manifold has topology R × S 2 and is constituted of homoclinic orbits which are bi-asymptotic to the S 3 center-center manifold. This is an invariant signature of chaos in the model, and produces chaotic sets in phase space. The model also presents an asymptotic DeSitter attractor at infinity and initial conditions sets are shown to have fractal basin boundaries connected to the escape into the DeSitter configuration (escape into inflation), characterizing the critical point as a chaotic scatterer.The longtime debate on the chaotic dynamics of general Bianchi IX models started with the work of Belinskii, Khalatnikov and Lifshitz (BKL) on * Electronic address: henrique@fnal.gov † Electronic address: ozorio@cbpf.br ‡ Electronic address: ivano@cbpf.br § Electronic address: tonini@etfes.br the oscillatory behaviour of such models in their approach to the singularity [1]. They showed that the approach to the singularity(t → 0) of a general Bianchi IX cosmological solution is an oscillatory mode, consisting of an infinite sequence of periods (called Kasner eras) during which two of the scale functions oscillate and the third one decreases monotonically; on passing from one era to another the monotonic behaviour is transfered to another of the three scale functions. The length of

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 the full nonlinear dynamics of closed FRW universes in the framework of D-branes formalism. Friedmann equations contain additional terms arising from the bulk-brane interaction that provide a concrete model for nonsingular bounces in the early phase of the universe. We construct nonsingular cosmological scenarios sourced with perfect fluids and a massive inflaton field which are past eternal, oscillory and may emerge into an inflationary phase due to nonlinear resonance mechanisms. Oscillatory behaviour becomes metastable when the system is driven into a resonance window of the parameter space of the models, with consequent break-up of KAM tori that trap the inflaton, leading the universe to the inflationary regime. A construction of the resonance chart of the models is made. Resonance windows are labeled by an integer n ≥ 2, where n is related to the ratio of the frequencies in the scale factor/scalar field degrees of freedom. They are typically small compared to volume of the whole parameter space, and we examine the constraints imposed by nonlinear resonance in the physical domain of initial configurations so that inflation may be realized. We discuss the complex dynamics arising in this pre-inflationary stage, the structural stability of the resonance pattern and some of its possible imprints in the physics of inflation. We also approach the issue of initial configurations that are connected to a chaotic exit to inflation. Pure scalar field bouncing cosmologies are constructed. Contrary to models with perfect fluid components, the structure of the bouncing dynamics is highly sensitive to the initial amplitude and to the mass of the inflaton; dynamical potential barriers allowing for bounces appear as a new feature of the dynamics. We argue that if our actual Universe is a brane inflated by a parametric resonance mechanism triggered by the inflaton, some observable cosmological parameters should then have a signature of the particular resonance from which the brane inflated.

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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.

In this paper we explore one of the most important features of the Galerkin method, which is to achieve high accuracy with a relatively modest computational effort, in the dynamics of RobinsonTrautman spacetimes.

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The dynamics of closed Friedmann–Robertson–Walker (FRW) universes with a massive inflaton field is examined where Friedmann equations are corrected by the introduction of a potential term that implements non-singular bounces in the early evolution of the universe. This potential term arises from quantum gravity/high-energy corrections to cosmological scenarios near the singularity and is semiclassical in nature, being effective only when the scale factor is very small. For certain windows in the parameter space labelled by the scalar field mass and the conserved Hamiltonian, nonlinear resonance phenomena take place. Nonlinear resonance may induce the destruction of Kolmogorov–Arnold–Moser (KAM) tori that trap the inflaton, leading to a rapid growth of the scale factor and the scalar field, with disruption of metastable states and consequent escape of the universe into inflation. We make a numerical/analytical approach to the nonlinear resonance phenomena, characterizing a particular resonance by its characteristic periodic orbits and by the structure of the associated diffusion pattern. The diffusion occurs when the orbit escapes through a Cantorus in the border of primary KAM islands that encloses the characteristic periodic orbits of the resonance. The windows of parametric resonance, characterized by an integer n ≥ 2 (associated with the ratio of the frequencies in the scale factor/scalar field degrees of freedom) are the ones that strongly favour inflation in the system. We discuss how generic this behaviour is for inflationary models, and its possible consequences for structure formation.