Convergence to a self-similar solution in general relativistic gravitational collapse

TL;DR

This paper demonstrates that in spherical gravitational collapse of a perfect fluid with specific equations of state, solutions tend to a self-similar form near singularities, providing insights into cosmic censorship and critical phenomena.

Contribution

It shows that generic collapse converges to a known self-similar solution, with implications for cosmic censorship and critical phenomena in gravitational collapse.

Findings

Collapse converges to the Larson-Penston self-similar solution near singularities.

Naked singularities can form, challenging cosmic censorship.

Critical phenomena with a specific exponent are predicted in Newtonian collapse.

Abstract

We study the spherical collapse of a perfect fluid with an equation of state $P=k\rho$ by full general relativistic numerical simulations. For $0<k\alt 0.036$, it has been known that there exists a general relativistic counterpart of the Larson-Penston self-similar Newtonian solution. The numerical simulations strongly suggest that, in the neighborhood of the center, generic collapse converges to this solution in an approach to a singularity and that self-similar solutions other than this solution, including a ``critical solution'' in the black hole critical behavior, are relevant only when the parameters which parametrize initial data are fine-tuned. This result is supported by a mode analysis on the pertinent self-similar solutions. Since a naked singularity forms in the general relativistic Larson-Penston solution for $0<k\alt0.0105$, this will be the most serious known counterexample against cosmic censorship. It also provides strong evidence for the self-similarity hypothesis in general relativistic gravitational collapse. The direct consequence is that critical phenomena will be observed in the collapse of isothermal gas in Newton gravity, and the critical exponent $\gamma$ will be given by $\gamma\approx 0.11$, though the order parameter cannot be the black hole mass.