On existence of matter outside a static black hole

TL;DR

This paper rigorously proves that perfect fluid matter cannot exist at rest outside a static black hole in asymptotically flat spacetimes without assuming spherical symmetry, under certain mass relation conditions.

Contribution

It provides the first non-spherical proof of the non-existence of static perfect fluid matter outside black holes under specific conditions.

Findings

Perfect fluid matter cannot be at rest outside static black holes.

The proof applies without assuming spherical symmetry.

Results relate stellar mass and black hole mass constraints.

Abstract

It is expected that matter composed of a perfect fluid cannot be at rest outside of a black hole if the spacetime is asymptotically flat and static (non-rotating). However, there has not been a rigorous proof for this expectation without assuming spheical symmetry. In this paper, we provide a proof of non-existence of matter composed of a perfect fluid in static black hole spacetimes under certain conditions, which can be interpreted as a relation between the stellar mass and the black hole mass.