Charged Vaidya Solution Satisfies Weak Energy Condition

TL;DR

This paper revisits the charged Vaidya solution, demonstrating it satisfies the weak energy condition through a new interpretation, and extends the analysis to higher dimensions, AdS spaces, and f(R) theories, with detailed exploration of specific mass-charge relations.

Contribution

The study extends Ori's interpretation of charged Vaidya solutions satisfying the weak energy condition to higher dimensions, AdS backgrounds, and higher-derivative gravity theories.

Findings

The external stress-tensor vanishes on a spacelike surface between horizons.

The interpretation holds in higher dimensions and AdS settings.

Specific mass-charge proportionality conditions ensure energy condition satisfaction.

Abstract

The external matter stress-tensor supporting charged Vaidya solution appears to violate weak energy condition in certain region of the spacetime. Motivated by this, a new interpretation of charged Vaidya solution was proposed by Ori [1] in which the energy condition continues to be satisfied. In this construction, one glues an outgoing Vaidya solution to the original ingoing Vaidya solution provided the surface where the external stress-tensor vanishes is spacelike. We revisit this study and extend it to higher-dimensions, to AdS settings, and to higher-derivative f(R) theories. In asymptotically flat space context, we explore in detail the case when the mass function m(v) is proportional to the charge function q(v). When the proportionality constant \nu = q(v)/m(v) lies in between zero and one, we show that the surface where the external stress-tensor vanishes is spacelike and lies in between the inner and outer apparent horizons.