No short hair behaviors of ultra-compact stars

Abstract

In the black hole spacetime, a no short hair theorem was proved, which states that the effective radius of black hole hairs must extend beyond the null circular orbit. In the present paper, in the horizonless gravity, we find a similar no short hair behavior that the effective radius of matter fields must also extend beyond the null circular orbit of ultra-compact stars. We should emphasize that the theorem presented in this manuscript is valid only for spatially regular matter configurations whose energy-momentum traces are non-negative.