Critical collapse of an axisymmetric ultrarelativistic fluid in $2+1$ dimensions

Abstract

We carry out numerical simulations of the gravitational collapse of a rotating perfect fluid with the ultrarelativistic equation of state $P=\kappa \rho$, in axisymmetry in $2+1$ spacetime dimensions with $\Lambda <0$. We show that for $\kappa \lesssim 0.42$, the critical phenomena are type I and the critical solution is stationary. The picture for $\kappa \gtrsim 0.43$ is more delicate: for small angular momenta, we find type II phenomena and the critical solution is quasistationary, contracting adiabatically. The spin-to-mass ratio of the critical solution increases as it contracts, and hence so does that of the black hole created at the end as we fine-tune to the black-hole threshold. Forming extremal black holes is avoided because the contraction of the critical solution smoothly ends as extremality is approached.

arXiv comment14 pages, 8 figures. Typos corrected. This version has been accepted by PRD

References in corpus (12)

• The Black Hole in Three Dimensional Space Time
• Critical phenomena in gravitational collapse
• Gravitational collapse in 2+1 dimensional AdS spacetime
• Critical gravitational collapse of a perfect fluid: nonspherical perturbations
• Critical collapse of rotating radiation fluids
• Scalar field critical collapse in 2+1 dimensions
• Critical gravitational collapse with angular momentum II: soft equations of state
• Extension of Kodama vector and quasilocal quantities in three-dimensional axisymmetric spacetimes
• Critical collapse of a rotating scalar field in $2+1$ dimensions
• Rigidly rotating perfect fluid stars in $2+1$ dimensions
• Fully constrained, high-resolution shock-capturing, formulation of the Einstein-fluid equations in $2+1$ dimensions
• Critical collapse of a spherically symmetric ultrarelativistic fluid in $2+1$ dimensions

Cited by in corpus (2)

• On the Dynamical Instability of Monatomic Fluid Spheres in (N+1)-Dimensional Spacetime
• The two-body problem in 2+1 spacetime dimensions with negative cosmological constant: two point particles