Quantum fields on semi-globally hyperbolic space-times

Abstract

We introduce a class of space-times modeling singular events such as evaporating black holes and topology changes, which we dub as semi-globally hyperbolic space-times. On these space-times we aim to study the existence of reasonable quantum field theories. We establish a notion of linear scalar quantum field theories on these space-times, show how such a theory might be constructed and introduce notions of global dynamics on these theories. Applying these constructions to both black hole evaporation and topology changing space-times, we find that existence of algebras can be relatively easily established, while the existence of reasonable states on these algebras remains an unsolved problem.

arXiv comment36 pages, 5 figures; added references in introduction, removed unnecessary assumption from definition 2.4, fixed some typo's

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Cited by in corpus (3)

• Hadamard states on spherically symmetric characteristic surfaces, the semi-classical Einstein equations and the Hawking effect
• ADM mass in warp drive spacetimes
• Topology change with Morse functions: progress on the Borde-Sorkin conjecture