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Slowly rotating gravastars

We solve Einstein's equations for slowly-rotating gravitational condensate stars (gravastars) up to second order in the rotation by expanding about the spherically symmetric gravastar with de Sitter interior and Schwarzschild exterior matched at their common horizon. Requiring that the perturbations are finite on the null surface reduces the exterior geometry to that of a Kerr black hole, implying that a slowly rotating gravastar cannot be distinguished from a Kerr black hole by any measurement or observation restricted to the macroscopic spacetime exterior to the horizon. We determine the interior solution, the surface stress tensor, and the Komar mass and angular momentum localized on the slowly rotating horizon surface. With the interior equation of state fixed at $p=-ρ$, finite junction conditions on the null horizon surface necessarily lead to an interior solution with a singular core, where the perturbative expansion breaks down. Comparison to other models and implications for more rapidly rotating gravastars are briefly discussed.