The 2m <= r property of spherically symmetric static spacetimes

TL;DR

This paper proves that spherically symmetric static spacetimes satisfying certain regularity and energy conditions cannot contain black holes, ensuring the 2m/r <= 1 property holds everywhere, even with matching hypersurfaces.

Contribution

It generalizes previous results by Baumgarte and Rendall to include non-isotropic matter and spacetimes with matching hypersurfaces, establishing a universal 2m/r <= 1 condition.

Findings

No black hole regions in the specified spacetimes.

The 2m/r <= 1 property holds everywhere under the given conditions.

Extension of previous perfect fluid results to non-isotropic cases.

Abstract

We prove that all spherically symmetric static spacetimes which are both regular at r=0 and satisfying the single energy condition rho + p_r + p_t >= 0 cannot contain any black hole region (equivalently, they must satisfy 2m/r <= 1 everywhere). This result holds even when the spacetime is allowed to contain a finite number of matching hypersurfaces. This theorem generalizes a result by Baumgarte and Rendall when the matter contents of the space-time is a perfect fluid and also complements their results in the general non-isotropic case.