A systematic approach to find solutions of the Einstein–Maxwell field equations for static spherically symmetric spacetimes using Segre classification

Abstract

In the literature, several spherically symmetric static solutions of the Einstein–Maxwell field equations (EMFEs) have been obtained by taking assumptions/ansatz on the parameters involved, like electric field intensity, gravitational potential, equation of state, etc. In this paper, using the Segre classification, we present a systematic scheme that limits the number of assumptions/ansatz required to be taken. It is found that the static spherically symmetric solutions of the EMFEs can only be of Segre types [Formula: see text], [Formula: see text], [Formula: see text], or [Formula: see text]. It is also shown that the type [Formula: see text] leads to the Schwarzschild de-Sitter/anti de-Sitter solutions.