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 contructions 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.

ADM mass in warp drive spacetimes

“…An added difficulty is that a superluminal warp drive comfortably overstays its welcome in the well-established field of curved space-time quantum field theory, as it cannot be globally hyperbolic [18]. While there is movement beyond global hyperbolicity (see, for example, [55]), one could still opt for the full glory: Dealing with the full semi-classical Einstein equations involving a quantized field on a (backreacting) background space-time [56,57]. While this would certainly (finally) address and answer the begged question of the usual invocation of arbitrarily advanced civilizations/magic by nebulous statements such as "the negative energy densities would have to be provided by quantum matter"-here be dragons, indeed.…”

Quantum fields on semi-globally hyperbolic space-times

“…Firstly I'd like to thank Prof. Dr. Klaas Landsman, under whose supervision I wrote my Master thesis [25] that became the foundations of this paper. Secondly I want to thank my doctoral advisor, Prof. Dr. Rainer Verch, under whose supervision I was able to expand on this thesis and write this paper.…”

A Role for the Fauxrizon in the Semiclassical Limit of a Fuzzball

“…This exposition should highlight one sense in which global hyperbolicity is not necessary for determinism. For more, seeFriedman (2004).8 That being said, efforts are ongoing to construct quantum field theories on various types of non-globally hyperbolic spacetimes, including those with timelike boundaries(Benini, Dappiaggi, and Schenkel 2018) or, indeed as are relevant here, for evaporating spacetimes and the case of spatial topology change(Janssen 2022). (I am grateful to an anonymous reviewer for this final reference.…”