We study the spherical collapse of a perfect fluid with an equation of state $P=k\rho$ by full general relativistic numerical simulations. For $0<k\lesssim 0.036,$ 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 $0<k\lesssim 0.0105,$ 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.

• Received 14 November 2000

DOI:https://doi.org/10.1103/PhysRevD.63.084022