On exact static spherically symmetric solutions in general relativity, Einstein-Cartan theory and higher-dimensional theories

Abstract

The equations describing the hydrostatic equilibrium of a static general relativistic fluid sphere are obtained for magnetofluids, Einstein-Cartan theory and anisotropic fluids in four dimensions and perfect fluids in D (D ≥ 4) dimensions. The method due to Hojman and Santamarina and Berger et al. is used to obtain a new and larger class of solutions. Illustrative examples have been given which lead to generalization of the Schwarschild exterior solution and the relativistic models for spiral galaxies and dense stars (Hojman et al.).