Regular black holes and energy conditions

We establish the relationship between the space-time structure of regular spherically-symmetrical black holes and the character of violation of the strong energy condition (SEC). It is shown that it is violated in any static region under the event horizon in such a way that the Tolman mass is negative there. In non-static regions there is constraint of another kind which, for a perfect fluid, entails violation of the dominant energy condition. (c) 2010 Elsevier B.V. All rights reserved.