Fluidos perfeitos estáticos com simetrias

• Autor(a) principal: Barboza, Marcelo Bezerra
• Data de Publicação: 2019
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/9570
• topic: Equação de Einstein; Fluido perfeito; Variedade estática; Simetria; Einstein equation; Perfect fluid; Static manifold; Symmetry; CIENCIAS EXATAS E DA TERRA::MATEMATICA

This work presents a two step procedure that is virtually capable of producing an infinite number of exact solutions to Einstein's equation of a perfect fluid on a static manifold. These steps could roughly be described as: 1) classifying the symmetries of the referred equation that convert it into a second order non linear ordinary differential equation of very specific nature -- whose solutions are a whole lot easier to come up with than those of the original problem, and 2) solving this ordinary equation -- which quite explains the need for the word `virtually' above, since not all solutions of the ordinary equation are known to its exact form. Finally, in the last chapter, we utilize a Theorem due to Liouville to determine the rigid motions of Riemannian metrics on euclidean space that do admit symmetries in a translational group and also belong to the conformal class of the flat metric.