Quantum fields on semi-globally hyperbolic space-times

TL;DR

This paper introduces semi-globally hyperbolic space-times to model singular events like black hole evaporation and topology change, exploring quantum field theory existence and dynamics on these complex backgrounds.

Contribution

It defines a new class of space-times and develops a framework for quantum field theories on them, highlighting challenges in state existence.

Findings

Existence of quantum field algebras is relatively straightforward.

Constructing reasonable states on these algebras remains unresolved.

The framework applies to black hole evaporation and topology change scenarios.

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.