General Dynamical Equations for Dingle’s Space-Times Filled with a Charged Non-perfect Fluid

Abstract

In this paper we have assumed charged non-perfect fluid as the material content of the space-time. The expression for the “mass function-M(r,y,z,t)” is obtained for the general situation and the contributions from the Ricci tensor in the form of material energy density ρ, pressure anisotropy $[\frac{p_{2}+p_{3}}{2}-p_{1}]$ , electromagnetic field energy ℰ and the conformal Weyl tensor, viz. energy density of the free gravitational field e $(=\frac{-3\Psi_{2}}{4\pi})$ are made explicit. This work is an extension of the work obtained earlier by Rao and Hasmani (Math. Today XIIA:71, 1993; New Directions in Relativity and Cosmology, Hadronic Press, Nonantum, 1997) for deriving general dynamical equations for Dingle’s space-times described by this most general orthogonal metric, $$ds^2=\exp(\nu)dt^2-\exp(\lambda)dr^2-\exp(2\alpha)dy^2-\exp(2\beta)dz^2,$$ where ν, λ, α and β are functions of all four space-time variables r, y, z and t.