(2+1) dimensional stars

TL;DR

This paper explores (2+1) dimensional gravity with rotating perfect fluid sources, revealing conditions for physically realistic solutions, including black hole-like exteriors and bounded source masses, with special cases like static and Godel-like geometries.

Contribution

It provides a comprehensive analysis of stationary, rotationally symmetric perfect fluid solutions in (2+1) dimensions, including integrability, matching conditions, and explicit solutions with physical insights.

Findings

Negative cosmological constant favors physically realistic solutions.

Static sources have bounded masses, often equal to one when the cosmological constant is zero.

Pressure inclusion improves physical plausibility of the models.

Abstract

We investigate, in the framework of (2+1) dimensional gravity, stationary, rotationally symmetric gravitational sources of the perfect fluid type, embedded in a space of arbitrary cosmological constant. We show that the matching conditions between the interior and exterior geometries imply restrictions on the physical parameters of the solutions. In particular, imposing finite sources and absence of closed timelike curves privileges negative values of the cosmological constant, yielding exterior vacuum geometries of rotating black hole type. In the special case of static sources, we prove the complete integrability of the field equations and show that the sources' masses are bounded from above and, for vanishing cosmological constant, generally equal to one. We also discuss and illustrate the stationary configurations by explicitly solving the field equations for constant mass--energy densities. If the pressure vanishes, we recover as interior geometries Godel like metrics defined on causally well behaved domains, but with unphysical values of the mass to angular momentum ratio. The introduction of pressure in the sources cures the latter problem and leads to physically more relevant models.