Hydrodynamic equilibrium of a static star in the presence of a cosmological constant in 2 + 1 dimensions

TL;DR

This paper investigates the conditions for static, circularly symmetric stars in (2+1) dimensions with a cosmological constant, deriving metrics and clarifying previous inaccuracies in the literature.

Contribution

It establishes hydrodynamic equilibrium conditions in (2+1) dimensions with a cosmological constant and corrects prior errors in related studies.

Findings

No lower bounds on pressure and mass, only positivity constraints.

Derived metric for constant density distribution.

Matched internal solution with external static solution with negative cosmological constant.

Abstract

Under the hydrodynamic equilibrium Buchdahl's conditions on the behavior of the density and the pressure, for regular fluid static circularly symmetric star in (2 + 1) dimensions in the presence of a cosmological constant, is established that there are no bounds from below on the pressure and also on the mass, except for their positiveness. The metric for a constant density distribution is derived and its matching with the external static solution with a negative cosmological constant is accomplished. Some mistakes of previous works on the topic are pointed out.