  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.
