Topology Change and Causal Continuity

TL;DR

This paper examines the issues of topology change in quantum gravity, focusing on causal discontinuities and their impact on spacetime singularities, by analyzing various topology-changing transitions.

Contribution

It investigates the conjecture that only certain types of topology change, characterized by causal discontinuities, cause problematic singularities in quantum gravity.

Findings

Causal discontinuities are linked to problematic singularities in topology change.

Not all topology changes necessarily lead to singularities or energy bursts.

Analysis of black hole pair production and geon formation supports the conjecture.

Abstract

The result that, for a scalar quantum field propagating on a ``trousers'' topology in 1+1 dimensions, the crotch singularity is a source for an infinite burst of energy has been used to argue against the occurrence of topology change in quantum gravity. We draw attention to a conjecture due to Sorkin that it may be the particular type of topology change involved in the trousers transition that is problematic and that other topology changes may not cause the same difficulties. The conjecture links the singular behaviour to the existence of ``causal discontinuities'' in the spacetime and relies on a classification of topology changes using Morse theory. We investigate various topology changing transitions, including the pair production of black holes and of topological geons, in the light of these ideas.