THE TOLMAN–OPPENHEIMER–VOLKOFF EQUATIONS AND THE SPACETIME PROPERTIES OF THE SCHWARZSCHILD–DE SITTER CONSTANT DENSITY INTERIOR SOLUTION

Abstract

In this paper, we first deduce the Tolman–Oppenheimer–Volkoff (TOV) equations and Schwarzschild–de Sitter (SdS) constant-density interior solutions of perfect fluid spheres in hydrostatic equilibrium by the Einstein equations with a nonzero cosmological constant. The TOV equations and the spacetime properties of exact solutions inside uniform perfect fluid spheres with different spatial curvature and cosmological constants will be respectively analyzed in detail. Moreover, a brief comparison between the internal static solutions of the SdS type and the dynamical Einstein–Strauss–de Sitter (ESdS) vacuole spacetime is obtained.