Slowly rotating ultracompact Schwarzschild star in the gravastar limit

TL;DR

This paper investigates the properties of slowly rotating ultracompact Schwarzschild stars near the gravastar limit, showing their exterior spacetime closely resembles Kerr black holes, making observational distinction challenging.

Contribution

It demonstrates that in the gravastar limit, a slowly rotating Schwarzschild star's metric converges to the Kerr metric, highlighting the difficulty in distinguishing these objects observationally.

Findings

The metric of a slowly rotating Schwarzschild star approaches the Kerr metric near the gravastar limit.

Surface and integral properties are computed using Hartle-Thorne equations at second order in angular velocity.

Observationally, gravastars and Kerr black holes are indistinguishable in this approximation.

Abstract

We reconsider the problem of a slowly rotating homogeneous star, or Schwarzschild star, when its compactness goes beyond the Buchdahl bound and approaches the gravastar limit $R\to 2M$. We compute surface and integral properties of such configuration by integrating the Hartle-Thorne structure equations for slowly rotating relativistic masses, at second order in angular velocity. In the gravastar limit, we show that the metric of a slowly rotating Schwarzschild star agrees with the Kerr metric, thus, within this approximation, it is not possible to tell a gravastar from a Kerr black hole by any observations from the spacetime exterior to the horizon.