Stellar Equilibrium in 2+1 Dimensions

TL;DR

This paper investigates the hydrostatic equilibrium of perfect fluid stars in 2+1 dimensions with anti-de Sitter asymptotics, deriving an upper mass limit and presenting exact solutions for uniform density cases.

Contribution

It introduces a new interior solution for 2+1 dimensional stars and establishes an upper mass limit analogous to Buchdahl's theorem.

Findings

An upper mass limit for 2+1 dimensional stars is derived.

Exact solutions for uniform density stars are provided.

The interior geometry matches the exterior black-hole solution.

Abstract

The hydrostatic equilibrium of a $2+1$ dimensional perfect fluid star in asymptotically anti-de Sitter space is discussed. The interior geometry matches the exterior $2+1$ black-hole solution. An upper mass limit is found, analogous to Buchdahl's theorem in 3+1, and the possibility of collapse is discussed. The case of a uniform matter density is solved exactly and a new interior solution is presented.