Very strong electromagnetic fields are characterized by the appearance of non-linearities. In order to explore the consequences of such non-linearities we have solved exactly the combined gravitational non-linear electromagnetic field equations for a static and spherical symmetric spacetime, where the source of the curvature is a point electric charge. We have chosen a non-linear Lagrangian density in such a way that the Maxwell, the Born--Infeld, and the Heisenberg--Euler theories are included as particular cases. The general solution can represent a charged black hole with the same characteristics of the Reissner--Nordstrø m one (two horizons and timelike singularity), or it can have only one horizon and a spacelike singularity, as in the Schwarzschild solution.

This work deals with the presence of topological defects in k-field models, where the dynamics is generalized to include higher order power in the kinetic term. We investigate kinks in (1,1) dimensions and vortices in (2,1) dimensions, focusing on some specific features of the solutions. In particular, we show how the kinks and vortices change to compactlike solutions, controlled by the parameter used to introduce the generalized models.Comment: 7 pages, 7 figures. Version to be published in PR

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We study the dynamics of anisotropic Bianchi type-IX models with matter and cosmological constant. The models can be thought as describing the role of anisotropy in the early stages of inflation, where the cosmological constant Λ plays the role of the vacuum energy of the inflaton field. The concurrence of the cosmological constant and anisotropy are sufficient to produce a chaotic dynamics in the gravitational degrees of freedom, connected to the presence of a critical point of saddle-center type in the phase space of the system. In the neighborhood of the saddle-center, the phase space presents the structure of cylinders emanating from unstable periodic orbits. The non-integrability of the system implies that the extension of the cylinders away from this neighborhood has a complicated structure arising from their transversal crossings, resulting in a chaotic dynamics. The invariant character of chaos is guaranteed by the topology of cylinders. The model also presents a strong asymptotic de Sitter attractor but the way out from the initial singularity to the inflationary phase is completely chaotic. For a large set of initial conditions, even with very small anisotropy, the gravitational degrees of freedom oscillate a long time in the neighborhood of the saddle-center before recollapsing or escaping to the de Sitter phase. These oscillations may provide a resonance mechanism for amplification of specific wavelengths of inhomogeneous fluctuations in the models. A geometrical interpretation is given for Wald's inequality in terms of invariant tori and their destruction by increasing values of the cosmological constant.

We examine the solutions of the equations of motion for an expanding Universe, taking into account the radiation of the inflaton field energy. We then analyze the question of the generality of inflationary solutions in this more general setting of a dissipative system. We find a surprisingly rich behavior for the solutions of the dynamical system of equations in the presence of dissipational effects. We also determine that a value of dissipation as small as ∼ 10 −7 H can lead to a smooth exit from inflation to radiation. PACS number(s): 98.80 Cq

Starting from a gauge invariant treatment of perturbations an analytical expression for the spectrum of long wavelength density perturbations in warm inflation is derived. The adiabatic and entropy modes are exhibited explicitly. As an application of the analytical results, we determined the observational constraint for the dissipation term compatible with COBE observation of the cosmic microwave radiation anisotropy for some specific models. In view of the results the feasibility of warm inflation is discussed.Comment: 11 pages, no figure

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.