Energy conditions for non-timelike thin shells

Abstract

We study energy conditions for non-timelike thin shells in arbitrary dimensions. It is shown that the induced energy–momentum tensor on a shell Σ is of the Hawking–Ellis type I if Σ is spacelike and either of type I, II, or III if Σ is null. Then, we derive simple equivalent representations of the standard energy conditions for . In particular, on a spacelike shell or on a null shell with non-vanishing surface current, inevitably violates the dominant energy condition. If the surface pressure on the null shell is vanishing in addition, is of type III and violates all the standard energy conditions. Those fully general results are obtained without imposing a spacetime symmetry and can be used in any theory of gravity. Lastly, several applications of the main results are presented in general relativity in four dimensions.