Slowly rotating ultra-compact Schwarzschild star in the gravastar limit

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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→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.