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 $\Lambda$, 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 $p(\rho )$. For any given equation of state, we find the two-parameter family of solutions with a regular centre 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 centre. Defining the dimensionless spin $\tilde{J}:=\sqrt{-\Lambda }J$, there is precisely one solution for each $(\tilde{J},M)$ in the region $|\tilde{J}|-1<M<|\tilde{J}|$, which consists of parts of the point particle region $M<-|\tilde{J}|$ and overspinning regions $|\tilde{J}|>|M|$. In an adjacent compact part of the black hole region $|\tilde{J}|<M$ (whose extent depends on the equation of state), there are precisely two solutions for each $(\tilde{J},M)$. Hence exterior solutions exist in all three classes of BTZ solution (black hole, point particle and overspinning), but not all possible values of $(\tilde{J},M)$ can be realised as stars. Regardless of the values of $\tilde{J}$ 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.

arXiv commentAdded references. This version accepted by PRD

References in corpus (8)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Stellar Equilibrium in 2+1 Dimensions
• The Anti-de Sitter Gott Universe: A Rotating BTZ Wormhole
• All Static Circularly Symmetric Perfect Fluid Solutions of 2+1 Gravity
• Gravitation vs. Rotation in 2+1 Dimensions
• (2+1) dimensional stars
• Polytropic stars in three-dimensional spacetime

Cited by in corpus (7)

• New black hole solutions in three-dimensional $f(R)$ gravity
• Fully constrained, high-resolution shock-capturing, formulation of the Einstein-fluid equations in $2+1$ dimensions
• Adiabatic analysis of the rotating BTZ black hole
• Critical collapse of a spherically symmetric ultrarelativistic fluid in $2+1$ dimensions
• Critical collapse of an axisymmetric ultrarelativistic fluid in $2+1$ dimensions
• Spinor solutions of a Chern-Simons model for the superconformal algebra
• The two-body problem in 2+1 spacetime dimensions with negative cosmological constant: two point particles