Charged Vaidya Solution Satisfies Weak Energy Condition

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 ν= 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.

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