Métodos espectrais aplicados à relatividade numérica: determinação dos dados iniciais

• Autor(a) principal: Alcoforado, Mariana Alves
• Data de Publicação: 2012
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/12912
• topic: Numerical relativity; Spectral methods; Black holes; Brill waves; Relatividade numérica; Métodos espectrais; Buracos negros; Ondas de Brill; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA GERAL::RELATIVIDADE E GRAVITACAO

In this work we apply spectral methods for determining the initial configuration of three spacetimes containing black holes. For this we present first the foliation of spacetime into three-dimensional spacelike hypersurfaces parameterized by the time function t. This process is called 3 + 1 decomposition [2] [5]. The result of this process are two sets of equations classified into constraint and evolution equations [4]. The constraint equations can be divided into Hamiltonian and momentum constraints.To obtain the initial data of the problems studied here, only the Hamiltonian constraint is solved numerically, since the momentum constraint of these cases have analytical solution. A short description of spectral methods is presented, highlighting Galerkin method, pseudospectral or collocation method and Tau method, which are employed in solving the constraint equations Hamiltonian of the problems studied. We found that the results obtained in this work outperform those produced by Kidder and Finn [15], due to a different choice of basis functions, which meet here one of the boundary conditions.