Black holes without singularities

Abstract

The conventional interpretation of the Hawking-Penrose singularity theorems is that gravitational collapse, signified by the presence of a closed trapped surface, generally leads to the formation of a singularity. Consideration is given here to an alternative interpretation according to which collapse scenarios may give rise, not to singularities, but to chronology violation instead. An example is given of a singularity-free, chronology-violating space-time with a (non-achronal) closed trapped surface. In a large class of singularity-free space-times, the presence of a closed trapped surface, achronal or not, necessitates a violation of chronology. Moreover, all closed trapped surfaces and chronology violations are confined to black holes; weak cosmic censorship must hold in the sense that the region of the space-time visible from infinity is globally hyperbolic.