Some properties of static general relativistic stellar models

Abstract

A number of properties of static general relativistic stellar models are presented which appear to be relevant to the ongoing search for a proof that all such models must have spherical symmetry. It is shown that any such model, having conformally flat spatial sections, must have spherical symmetry. A general procedure is described which allows one to construct the type of ’’divergence equals positive quantity’’ identities for static stellar models, which were used to prove that static black holes must have spherical symmetry. This procedure is used to produce a large new class of identities for the exterior vacuum regions of static stellar models and identities are constructed for the interior regions of uniform density models. These identities are used to prove that static uniform density stellar models must have spherical symmetry.