2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/195810It 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.4pages, final version accepted for publication in Journal of Mathematical PhysicsGeneral Relativity and Quantum CosmologyAstrophysicsDifferential Geometrytext