Critical collapse of a spherically symmetric ultrarelativistic fluid in $2+1$ dimensions

Abstract

We carry out numerical simulations of the gravitational collapse of a perfect fluid with the ultrarelativistic equation of state $P=\kappa \rho$, in spherical symmetry in $2+1$ spacetime dimensions with $\Lambda <0$. At the threshold of prompt collapse, we find type II critical phenomena (apparent horizon mass and maximum curvature scale as powers of distance from the threshold) for $\kappa \gtrsim 0.43$, and type I critical phenomena (lifetime scales as logarithm of distance from the threshold) for $\kappa \lesssim 0.42$. The type I critical solution is static, while the type II critical solution is not self-similar (as in higher dimensions) but contracting quasi-statically.

22 pages, 15 figures. Typos corrected. This version has been accepted by PRD

References in corpus (1)

• Rigidly rotating perfect fluid stars in $2+1$ dimensions

Cited by in corpus (3)

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