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.