Slowly rotating ultracompact Schwarzschild star in the gravastar limit

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.