No short hair behaviors of ultra-compact stars

TL;DR

This paper demonstrates that in horizonless ultra-compact stars, matter fields must extend beyond the null circular orbit, similar to black hole hair behavior, indicating a universal property of compact objects.

Contribution

It establishes a no short hair theorem for horizonless ultra-compact stars, extending the concept from black holes to these objects.

Findings

Matter fields extend beyond the null circular orbit.

No short hair behavior is present in horizonless ultra-compact stars.

The result suggests a universal property of compact objects.

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.