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It is expected that matter composed of a perfect fluid cannot be at restoutside of a black hole if the spacetime is asymptotically flat and static(non-rotating). However, there has not been a rigorous proof for thisexpectation without assuming spheical symmetry. In this paper, we provide aproof of non-existence of matter composed of a perfect fluid in static blackhole spacetimes under certain conditions, which can be interpreted as arelation between the stellar mass and the black hole mass.Comment: 4pages, final version accepted for publication in Journal of  Mathematical Physic

On existence of matter outside a static black hole