Can a Black Hole Collapse to a Space-time Singularity?

Abstract

A critique of the singularity theorems of Penrose, Hawking, and Geroch is given. It is pointed out that a gravitationally collapsing black hole acts as an ultrahigh energy particle accelerator that can accelerate particles to energies inconceivable in any terrestrial particle accelerator, and that when the energy $E$ of the particles comprising matter in a black hole is $\sim 10^{2} GeV$ or more, or equivalently, the temperature $T$ is $\sim 10^{15} K$ or more, the entire matter in the black hole is converted into quark-gluon plasma permeated by leptons. As quarks and leptons are fermions, it is emphasized that the collapse of a black-hole to a space-time singularity is inhibited by Pauli's exclusion principle. It is also suggested that ultimately a black hole may end up either as a stable quark star, or as a pulsating quark star which may be a source of gravitational radiation, or it may simply explode with a mini bang of a sort.