Gödel's universe and induced-matter theory

• Autor(a) principal: Fonseca-Neto,J. B.
• Data de Publicação: 2005
• Outros Autores: Romero,C., Dahia,F.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Brazilian Journal of Physics
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332005000700013

We discuss Gödel's universe in the context of the induced-matter theory. We show that the problem of generating Gödel's metric from an extra dimension is equivalent to finding an embedding of Gödel's universe in a Ricci-flat five-dimensional space. On the other hand, according to the Campbell-Magaard theorem, any spacetime can be locally embedded into a five-dimensional pseudo-Riemannian Ricci-flat manifold. We obtain explicitly a global embedding of Gödel's universe which is Ricci-flat and has a non-Lorentzian signature of type (++---).