The nature of the naked singularity in generalized Vaidya spacetime and white hole geodesics

Abstract

This paper gives conditions to the energy-momentum tensor when the gravitational collapse of generalized Vaidya spacetime results in a naked singularity. We also consider the gravitational collapse of a matter cloud whose interior is described with Vaydia-de Sitter spacetime—when the collapse ends, this metric must be the de Sitter one, and the result of such a collapse is a so-called regular black hole. We provide the geodesic equations for the case when the matter is described with the equation of the state both P = −ρ and P = αρ, where α belongs to the interval (0,1/3]. We match these geodesics with geodesics in the Schwarzschild metric. We also explain the nature of white hole geodesics with either the naked singularity formation or the regular black hole formation.