scholarly journals Constant Mean Curvature Foliations of Globally Hyperbolic Spacetimes Locally Modelled on AdS 3

2006 ◽  
Vol 126 (1) ◽  
pp. 71-129 ◽  
Author(s):  
Thierry Barbot ◽  
François Béguin ◽  
Abdelghani Zeghib
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Globally Hyperbolic ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes

scholarly journals Global wave parametrices on globally hyperbolic spacetimes

2020 ◽  
Vol 490 (2) ◽  
pp. 124316
Author(s):  
Matteo Capoferri ◽  
Claudio Dappiaggi ◽  
Nicolò Drago
Keyword(s):  
Globally Hyperbolic ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes

scholarly journals Abelian Duality on Globally Hyperbolic Spacetimes

2016 ◽  
Vol 349 (1) ◽  
pp. 361-392 ◽  
Author(s):  
Christian Becker ◽  
Marco Benini ◽  
Alexander Schenkel ◽  
Richard J. Szabo
Keyword(s):  
Globally Hyperbolic ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes

THE PRINCIPLE OF LOCALITY AND QUANTUM FIELD THEORY ON (NON GLOBALLY HYPERBOLIC) CURVED SPACETIMES

1992 ◽  
Vol 04 (spec01) ◽  
pp. 167-195 ◽  
Author(s):  
BERNARD S. KAY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Field Algebra ◽  
Massless Field ◽  
Globally Hyperbolic ◽  
Local Algebras ◽  
Hyperbolic Spacetime ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes

In the context of a linear model (the covariant Klein Gordon equation) we review the mathematical and conceptual framework of quantum field theory on globally hyperbolic spacetimes, and address the question of what it might mean to quantize a field on a non globally hyperbolic spacetime. Our discussion centres on the notion of F-locality which we introduce and which asserts there is a net of local algebras such that every neighbourhood of every point contains a globally hyperbolic subneighbourhood of that point for which the field algebra coincides with the algebra one would obtain were one to regard the subneighbourhood as a spacetime in its own right and quantize — with some choice of time-orientation — according to the standard rules for quantum field theory on globally hyperbolic spacetimes. We show that F-locality is a property of the standard field algebra construction for globally hyperbolic spacetimes, and argue that it (or something similar) should be imposed as a condition on any field algebra construction for non globally hyperbolic spacetimes. We call a spacetime for which there exists a field algebra satisfying F-locality F-quantum compatible and argue that a spacetime which did not satisfy something similar to this condition could not arise as an approximate classical description of a state of quantum gravity and would hence be ruled out physically. We show that all F-quantum compatible spacetimes are time orientable. We also raise the issue of whether chronology violating spacetimes can be F-quantum compatible, giving a special model — a massless field theory on the “four dimensional spacelike cylinder” — which is F-quantum compatible, and a (two dimensional) model — a massless field theory on Misner space — which is not. We discuss the possible relevance of this latter result to Hawking’s recent Chronology Protection Conjecture.

Sign in / Sign up

Export Citation Format

Share Document