E. L. Rodrigues

Kolmogorov-Zakharov Spectrum in AdS Gravitational Collapse

We study black hole formation during the gravitational collapse of a massless scalar field in asymptotically D-dimensional anti-de Sitter AdS(D) spacetimes for D = 4, 5. We conclude that spherically symmetric gravitational collapse in asymptotically AdS spaces is turbulent and characterized by a Kolmogorov-Zakharov spectrum. Namely, we find that after an initial period of weakly nonlinear evolution, there is a regime where the power spectrum of the Ricci scalar evolves as ω(-s) with the frequency, ω, and s ≈ 1.7 ± 0.1.

Numerical evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method

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 provides high accuracy with moderate computational effort. Several numerical 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.

Numerical evolution of radiative Robinson-Trautman spacetimes

The evolution of spheroids of matter emitting gravitational waves and a 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 on is the mass extraction of the bounded configuration through the emission of both types of radiation.

Numerical evolution of general Robinson-Trautman spacetimes: code tests, wave forms and the efficiency of the gravitational wave extraction

We present an efficient numerical code based on spectral meth ods to integrate the field equations of general Robinson-Trautmann spacetimes. The most natural basis functions for the spectral expansion of the metric functions are spherical harmonics. Using the values of appropriate combinations of the metric functions at the collocation points, we have managed to reduce expression swell when the number of spherical harmonics increases. Our numerical code runs with relatively little c omputational resources and the code tests have shown excellent accuracy and convergence. The code has been applied to situations of physical interest in the context of Robsinson-Trautmann geometries such as: perturbation of the exterior gravitational field of a spheroid of matter; perturbation of an initially boosted black hole; an d the non-frontal collision of two Schwarzschild black holes. In dealing with these processes we have derived analytical lower and upper bounds on the velocity of the resulting black hole and the efficiency of the gravitational wave extraction, respectively. Numerical experiments were performed to determine the forms of the gravitational waves and the efficiency in each situation of interest.

THE LOW DIMENSIONAL DYNAMICAL SYSTEM APPROACH IN GENERAL RELATIVITY: AN EXAMPLE

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 Robinson–Trautman spacetimes.

Nonlinear evolution of cylindrical gravitational waves: numerical method and physical aspects

General cylindrical waves are the simplest axisymmetrical gravitational waves that contain both

A DYNAMICAL SYSTEM APPROACH FOR THE BONDI PROBLEM

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Nonlinear interaction between electromagnetic and gravitational waves: An appraisal

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Three-dimensional distorted black holes: Using the Galerkin-Collocation method

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BLACK HOLES COLLISION IN GENERAL ROBINSON-TRAUTMAN SPACETIMES: WAVE FORMS AND THE EFFICIENCY OF THE GRAVITATIONAL WAVE EXTRACTION

modes of polarization. In this paper, we have studied the evolution of general cylindrical gravitational waves in the realm of the characteristic scheme with a numerical code based on the Galerkin-Collocation method. The investigation consists of the numerical realization of concepts such as Bondi mass and the news functions adapted to cylindrical symmetry. The Bondi mass decays due to the presence of the news functions associated with both polarization modes. We have interpreted that each polarization mode as channels from which mass is extracted. Under this perspective, we have presented the enhancement effect of the polarization mode