Topology Change and Causal Continuity

Details Topology Change and Causal Continuity Topology Change and Causal Continuity

1997-11-23

arxiv.org/abs/gr-qc/9711070v2

Phys.Rev. D58 (1998) 124019

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 28 pages, 10 figures, small changes in text (one figure removed), conclusions remain unchanged. Accepted for publicatio

Scientific paper

10.1103/PhysRevD.58.124019

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.

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