Abstract:
We examine the dynamics of the gravitational collapse in a 4-dim Lorentzian brane embedded in a 5-dim bulk with an extra timelike dimension. By considering the collapse of pure dust on the brane we derive a bouncing FLRW interior solution and match it with a corrected Schwarzschild exterior geometry. In the physical domain considered for the parameters of the solution, the analytical extension is built, exhibiting an exterior event horizon and a Cauchy horizon, analogous to the Reissner-Nordstr\"om solution. For such an exterior geometry we examine the effects of the bulk-brane corrections in the Hawking radiation. In this scenario the model extends Bekenstein's black hole geometrical thermodynamics for quasi-extremal configurations, with an extra work term in the laws associated with variations of the brane tension. We also propose a simple statistical mechanics model for the entropy of the bouncing collapsed matter by quantizing its fluctuations and constructing the associated partition function. This entropy differs from the geometrical entropy by an additive constant proportional to the area of the extremal black hole and satisfies an analogous first law of thermodynamics. A possible connection between both entropies is discussed.

Abstract:
we construct a spacetime whose only source of curvature is a dirac magnetic monopole, and whose geometry inherits the structure of lines of singularities of the monopole electromagnetic potentials. the spacetime has the topology s3 × r, is stationary and asymptotically at but not asymptotically minkowskian, with its at null infinity having the topology of s3. these mild pathologies, as acausality and string structure, allow the spacetime configuration to have a gravitational magnetic mass, which results proportional to the charge m of the monopole. this suggests that the dirac monopole may be the source of magnetic mass in gravitational configurations, which has no newtonian analogue. alsom has the role of a nut parameter in the metric of the spacetime, suggesting that the charge of the monopole can provide a physical realization of the nut parameter.

Abstract:
We construct a spacetime whose only source of curvature is a Dirac magnetic monopole, and whose geometry inherits the structure of lines of singularities of the monopole electromagnetic potentials. The spacetime has the topology S3 x R, is stationary and asymptotically at but not asymptotically Minkowskian, with its at null infinity having the topology of S3. These mild pathologies, as acausality and string structure, allow the spacetime configuration to have a gravitational magnetic mass, which results proportional to the charge mu of the monopole. This suggests that the Dirac monopole may be the source of magnetic mass in gravitational configurations, which has no Newtonian analogue. Alsomu has the role of a NUT parameter in the metric of the spacetime, suggesting that the charge of the monopole can provide a physical realization of the NUT parameter.

Abstract:
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 $n \geq 2$, 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.

Abstract:
We examine the nonlinear dynamics of a closed Friedmann-Robertson-Walker universe in the framework of Brane World formalism with a timelike extra dimension. In this scenario, the Friedmann equations contain additional terms arising from the bulk-brane interaction which provide a concrete model for nonsingular bounces in the early phase of the Universe. We construct a nonsingular cosmological scenario sourced with dust, radiation and a cosmological constant. The structure of the phase space shows a nonsingular orbit with two accelerated phases, separated by a smooth transition corresponding to a decelerated expansion. Given observational parameters we connect such phases to a primordial accelerated phase, a soft transition to Friedmann (where the classical regime is valid), and a graceful exit to a de Sitter accelerated phase.

Abstract:
The dynamics of the gravitational collapse is examined in the realm of string based formalism of D-branes that encompass General Relativity as a low energy limit. A complete analytical solution is given to the spherically symmetric collapse of a pure dust star, including its matching with a corrected Schwarzschild exterior spacetime. The collapse forms a black hole (an exterior event horizon) enclosing not a singularity but perpetually bouncing matter in the infinite chain of spacetime maximal analytical extensions inside the outer event horizon. This chain of analytical extensions has a structure analogous to that of the Reissner-Nordstrom solution, except that the timelike singularities are avoided by bouncing barriers. The interior trapped bouncing matter has the possibility of being expelled by disruptive nonlinear resonance mechanisms.

Abstract:
A relativistic model for the emission of gravitational waves from an initially unperturbed Schwarzschild black hole, or spherical collapsing configuration, is completely integrated. The model consists basically of gravitational perturbations of the Robinson-Trautman type on the Schwarzschild spacetime. In our scheme of perturbation, gravitational waves may extract mass from the collapsing configuration. Robinson-Trautmann perturbations also include another mode of emission of mass, which we denote shell emission mode: in the equatorial plane of the configuration, a timelike $(1+2)$ shell of matter may be present, whose stress-energy tensor is modelled by neutrinos and strings emitted radially on the shell; no gravitational waves are present in this mode. The invariant characterization of gravitational wave perturbations and of the gravitational wave zone is made through the analysis of the structure of the curvature tensor and the use of the Peeling Theorem.

Abstract:
the relationship between ontogenetic variation of intestine length and feeding habits of five stream-dwelling fish species from the ubatiba river were investigated. analysed data were based on two size categories (juveniles and adults) and two food categories (animal and vegetal). diet composition of each size category revealed that astyanax janeiroensis and geophagus brasiliensis changed food preference throughout ontogeny and switched from omnivorous/carnivorous to omnivorous/herbivorous and from omnivorous/carnivorous to omnivorous, respectively. these changes were followed by ontogenetic changes in the intestinal coefficient (ic). no ontogenetic differences were registered for ic and food categories consumed by hoplias malabaricus but significant differences in the size of consumed preys as well as positive correlation between fish size (predator) and prey size was observed. food items (within animal category) consumed by the adult pimelodella lateristriga were mainly based on allochthonous arthropods whereas juvenile individuals fed with the same intensity on allochthonous and autochthonous arthropods; both juveniles and adult individuals of mimagoniates microlepis were mainly allochthonous feeders. mean ic values of pimelodella lateristriga and mimagoniates microlepis did not change along body growth. although changes in food category consumption were not common among all the studied species, changes in the resource exploitation strategy was a rule among them, except for mimagoniates microlepis.

Abstract:
We study the dynamics of a bounded gravitational collapsing configuration emitting gravitational waves, where the exterior spacetime is described by Robinson-Trautman geometries. The full nonlinear regime is examined by using the Galerkin method that allows us to reduce the equations governing the dynamics to a finite-dimensional dynamical system, after a proper truncation procedure. Amongst the obtained results of the nonlinear evolution, one of the most impressive is the fact that the distribution of the mass fraction extracted by gravitational wave emission satisfies the distribution law of nonextensive statistics and this result is independent of the initial configurations considered.

Abstract:
We examine numerically the post-merger regime of two Schwarzschild black holes in non head-on collision. Our treatment is made in the realm of non-axisymmetric Robinson-Trautman spacetimes which are appropriate for the description of the system. Characteristic initial data for the system are constructed and the Robinson-Trautman equation is integrated using a numerical code based on the Galerkin spectral method. The collision is planar, restricted to the plane determined by the directions of the two initial colliding black holes, with the net momentum fluxes of gravitational waves 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. Our analysis is based on the Bondi-Sachs four momentum conservation laws. Head-on collisions and orthogonal collisions constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extraction by gravitational waves. The momentum extraction and the pattern of the momentum fluxes, as a function of the incidence angle, are examined. The momentum extraction characterizes a regime of strong deceleration of the system. The angular pattern of gravitational wave signals is also examined. They are typically bremsstrahlung for early times emission. Gravitational waves are also emitted outside the plane of collision but this component has a zero net momentum flux. The relation between the incidence angle of collision and the exit angle of the remnant closely approximates a relation for inelastic collisions of classical particles in Newtonian dynamics.