New exact solutions for a charged fluid sphere in general relativity
This paper describes new techniques and results for the problem of the coupled Einstein-Maxwell equations with static spherical charge distributions, which might be a source for the well known exterior Reissner-Nordstrom exact solution. In this paper, the barytropic pressure proportional to density, equation of state is used for the matter. The resulting Einstein-Maxwell equations result in a nonlinear Riccati type equation. The authors show that a known particular solution can be used to reduce the equation to a simple linear one, which can be easily integrated to produce new solutions containing arbitrary constants. This approach is used to generate new solutions from particular ones given by other workers. One possible difficulty is guaranteeing that the resulting solution results in zero pressure at finite radius, which is of course required to join on to the exterior Reissner-Nordström solution.
static spherically symmetric distribution of charged fluids
exterior Reissner-Nordström exact solution
scientific article; zbMATH DE number 3954593