Rigidly rotating perfect fluid stars in 2+1 dimensions

Abstract

Cataldo has found all rigidly rotating self-gravitating perfect fluid solutions in 2+1 dimensions with a negative cosmological constant Λ, for a density that is specified a priori as a function of a certain radial coordinate. We rewrite these solutions in standard polar-radial coordinates, for an arbitrary barotropic equation of state p(ρ). For any given equation of state, we find the two-parameter family of solutions with a regular center and finite total mass M and angular momentum J (rigidly rotating stars). For analytic equations of state, the solution is analytic except at the surface, but including at the center. Defining the dimensionless spin ˜J≔√−ΛJ, there is precisely one solution for each (˜J,M) in the region |˜J|−1<M<|˜J|, which consists of parts of the point-particle region M<−|˜J| and overspinning regions |˜J|>|M|. In an adjacent compact part of the black-hole region |˜J|<M (whose extent depends on the equation of state), there are precisely two solutions for each (˜J,M). Hence, exterior solutions exist in all three classes of Bañados, Teitelboim, and Zanelli solution (black hole, point particle, and overspinning), but not all possible values of (˜J,M) can be realized as stars. Regardless of the values of ˜J and M, the causal structure of all stars for all equations of state is that of anti–de Sitter space, without horizons or closed timelike curves.

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Identifiers

ORCID for Carsten Gundlach: orcid.org/0000-0001-9585-5375

ORCID for Patrick Bourg: orcid.org/0000-0003-0015-0861

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