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arXiv · gr-qc/9406006

Topology Change in (2+1)-Dimensional Gravity

S. Carlip·R. Cosgrove
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Abstract

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial topology change are nonvanishing---in fact, they can be infrared divergent---but that they are infinitely suppressed relative to similar topology-preserving amplitudes.

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S. Carlip, R. Cosgrove. 1994-06-03. Topology Change in (2+1)-Dimensional Gravity. https://doi.org/10.1063/1.530760

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