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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We study energy conditions for non-timelike massive thin shells in arbitrary
$n(\ge 3)$ dimensions. It is shown that the induced energy-momentum tensor
$t_{\mu\nu}$ on a shell $\Sigma$ is of the Hawking-Ellis type I if $\Sigma$ is
spacelike and either of type I, II, or III if $\Sigma$ is null. Then, we derive
simple equivalent representations of the standard energy conditions for
$t_{\mu\nu}$. In particular, on a spacelike shell or on a null shell with
non-vanishing surface current, $t_{\mu\nu}$ inevitably violates the dominant
energy condition. 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.
