We present a model of two-kinks resulting from an explicit composition of two standards kinks of the $phi^4$ model based on the procedure of Ref. cite{uchiyama}. The two-kinks have an additional parameter accounting for the separation of the standard
kinks of $phi^4$ model. We have shown that the two-kinks have two discrete internal modes besides the zeroth mode and the continuous spectrum. This new feature signalizes that the head-on collision a two-kinks/two-antikinks pair exhibits a rich and complex behavior due to the additional channel from which the energy of the system can be stored. We have exhibited the fractal structure associated with the main configurations after the collision. We have inferred the fractality as the imprint of the nonlinear exchange of energy into the two discrete internal modes.
We present an implementation of the Galerkin-Collocation method to determine the initial data for non-rotating distorted three dimensional black holes in the inversion and puncture schemes. The numerical method combines the key features of the Galerk
in and Collocation methods which produces accurate initial data. We evaluated the ADM mass of the initial data sets, and we have provided the angular structure of the gravitational wave distribution at the initial hypersurface by evaluating the scalar $Psi_4$ for asymptotic observers.
We have investigated the head-on collision of a two-kink and a two-antikink pair that arises as a generalization of the $phi^4$ model. We have evolved numerically the Klein-Gordon equation with a new spectral algorithm whose accuracy and convergence
were attested by the numerical tests. As a general result, the two-kink pair is annihilated radiating away most of the scalar field. It is possible the production of oscillons-like configurations after the collision that bounce and coalesce to form a small amplitude oscillon at the origin. The new feature is the formation of a sequence of quasi-stationary structures that we have identified as lump-like solutions of non-topological nature. The amount of time these structures survives depends on the fine-tuning of the impact velocity.
In this work we have studied the nonlinear preheating dynamics of the $frac{1}{4} lambda phi^4$ inflationary model. It is well established that after a linear stage of preheating characterized by the parametric resonance, the nonlinear dynamics becom
es relevant driving the system towards turbulence. Wave turbulence is the appropriated description of this phase since matter distributions are fields instead of usual fluids. Therefore, turbulence develops due to the nonlinear interations of waves, here represented by the small inhomogeneities of the inflaton field. We present relevant aspects of wave turbulence such as the Kolmogorov-Zakharov spectrum in frequency and wave number domains that indicates that there are a transfer of energy through scales. From the power spectrum of the matter energy density we were able to estimate the temperature of the thermalized system.
We present the first numerical code based on the Galerkin and Collocation methods to integrate the field equations of the Bondi problem. The Galerkin method like all spectral methods provide high accuracy with moderate computational effort. Several n
umerical tests were performed to verify the issues of convergence, stability and accuracy with promising results. This code opens up several possibilities of applications in more general scenarios for studying the evolution of spacetimes with gravitational waves.
The evolution of spheroids of matter emitting gravitational waves and null radiation field is studied in the realm of radiative Robinson-Trautman spacetimes. The null radiation field is expected in realistic gravitational collapse, and can be either
an incoherent superposition of waves of electromagnetic, neutrino or massless scalar fields. We have constructed the initial data identified as representing the exterior spacetime of uniform and non-uniform spheroids of matter. By imposing that the radiation field is a decreasing function of the retarded time, the Schwarzschild solution is the asymptotic configuration after an intermediate Vaidya phase. The main consequence of the joint emission of gravitational waves and the null radiation field is the enhancement of the amplitude of the emitted gravitational waves. Another important issue we have touched is the mass extraction of the bounded configuration through the emission of both types of radiation.
