Topology Change and Causal Continuity

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.

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

References in corpus (1)

• A handlebody calculus for topology change

Cited by in corpus (39)

• Observations of Hawking radiation: the Page curve and baby universes
• Phantom stars and topology change
• Signature change events: A challenge for quantum gravity?
• Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
• On the geometrization of matter by exotic smoothness
• COBE and Global Topology: An Example of the Application of the Identified Circles Principle
• The residual gravity acceleration effect in the Poincare dodecahedral space
• Morse index and causal continuity. A criterion for topology change in quantum gravity
• K-causality and degenerate spacetimes
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Cosmic crystallography using short-lived objects - active galactic nuclei
• Boundary dynamics and topology change in quantum mechanics
• The Sorkin-Johnston State in a Patch of the Trousers Spacetime
• A causal perspective on random geometry
• A non-local way around the no-global-symmetries conjecture in quantum gravity?
• Transverse Galaxy Velocities from Multiple Topological Images
• Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
• Anisotropic Structures and Wormholes with Loop Quantum Gravity Holonomy Corrections
• A relativistic model of the topological acceleration effect
• Quantum Physics and Fluctuating Topologies: Survey
• Compactification, topology change and surgery theory
• On topological restrictions of the spacetime in cosmology
• On the origin of inflation by using exotic smoothness
• Analytic Results in 2D Causal Dynamical Triangulations: A Review
• Topological gravity on plumbed V-cobordisms
• Space-time foam in 2D and the sum over topologies
• Singularity at the demise of a black hole
• A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
• A topological model for inflation
• Topology change with Morse functions: progress on the Borde-Sorkin conjecture
• Gauge Group and Topology Change
• Finite energy quantization on a topology changing spacetime
• Which FLRW comoving 3-manifold is preferred observationally and theoretically?
• There was movement that was stationary, for the four-velocity had passed around
• Topological implications of inhomogeneity
• Causal structure and topology change in (2+1)-dimensional simplicial gravity
• Morse-Bott inequalities, Topology Change and Cobordisms to Nothing
• Observational Constraints on the Topology (Global Geometry) of the Universe
• Stress-Energy in the Conical Vacuum and its Implications for Topology Change