Topology change in (2+1)-dimensional gravity

1994/06/03 by S. Carlip, Steven Carlip, R. Cosgrove +1 · 3 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Classical mechanics #Combinatorics #Cosmology and Gravitation Theories #General relativity #Invariant (physics) #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Topology (electrical circuits) #gr-qc

paper · pdf · doi:10.1063/1.530760

published as J.Math.Phys.35:5477-5493,1994 · 19 pages of text plus 4 pages of figures, LaTeX (using epsf), UCD-11-94

arxiv created 1994/06/03 · openalex publication_date 1994/10/01 · arxiv updated 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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, the amplitude for a simple topology-changing process is evaluated. It is shown 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.

Citations

• Topology change in ISO(2, 1) Chern-Simons gravity
• 2 + 1 dimensional gravity as an exactly soluble system
• On the nature of quantum geometrodynamics

Cited by

• A phase space path integral for (2+1)-dimensional gravity
• A note on real tunnelling geometries
• The Ponzano–Regge model