Relevant bibliographies by topics / Non-Globally Hyperbolic Spacetimes

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Academic literature on the topic 'Non-Globally Hyperbolic Spacetimes'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Non-Globally Hyperbolic Spacetimes"

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KAY, BERNARD S. "THE PRINCIPLE OF LOCALITY AND QUANTUM FIELD THEORY ON (NON GLOBALLY HYPERBOLIC) CURVED SPACETIMES." Reviews in Mathematical Physics 04, spec01 (December 1992): 167–95. http://dx.doi.org/10.1142/s0129055x92000194.

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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.
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Seggev, Itai. "Dynamics in stationary, non-globally hyperbolic spacetimes." Classical and Quantum Gravity 21, no. 11 (April 29, 2004): 2651–68. http://dx.doi.org/10.1088/0264-9381/21/11/010.

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Ishibashi, Akihiro, and Robert M. Wald. "Dynamics in non-globally-hyperbolic static spacetimes: III. Anti-de Sitter spacetime." Classical and Quantum Gravity 21, no. 12 (May 19, 2004): 2981–3013. http://dx.doi.org/10.1088/0264-9381/21/12/012.

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Fewster, C. J., and A. Higuchi. "Quantum field theory on certain non-globally hyperbolic spacetimes." Classical and Quantum Gravity 13, no. 1 (January 1, 1996): 51–61. http://dx.doi.org/10.1088/0264-9381/13/1/006.

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BULLOCK, DAVID M. A. "KLEIN–GORDON SOLUTIONS ON NON-GLOBALLY HYPERBOLIC STANDARD STATIC SPACETIMES." Reviews in Mathematical Physics 24, no. 10 (November 2012): 1250028. http://dx.doi.org/10.1142/s0129055x12500286.

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We construct a class of solutions to the Cauchy problem of the Klein–Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a technical condition: "acceptability") of (some variant of) the Laplace–Beltrami operator defined on test functions in an L2-space of the static hypersurface. The proof of the existence of this construction completes and extends work originally done by Wald. Further results include: the uniqueness of these solutions; their support properties; the construction of the space of solutions and the energy and symplectic form on this space; an analysis of certain symmetries on the space of solutions; and various examples of this method, including the construction of a non-bounded below acceptable self-adjoint extension generating the dynamics.
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Duggal, K. L. "Space time manifolds and contact structures." International Journal of Mathematics and Mathematical Sciences 13, no. 3 (1990): 545–53. http://dx.doi.org/10.1155/s0161171290000783.

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A new class of contact manifolds (carring a global non-vanishing timelike vector field) is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic) spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.
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Yurtsever, Ulvi. "Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes." Classical and Quantum Gravity 11, no. 4 (April 1, 1994): 999–1012. http://dx.doi.org/10.1088/0264-9381/11/4/016.

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Rovenski, Vladimir. "Einstein-Hilbert type action on spacetimes." Publications de l'Institut Math?matique (Belgrade) 103, no. 117 (2018): 199–210. http://dx.doi.org/10.2298/pim1817199r.

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The mixed gravitational field equations have been recently introduced for codimension one foliated manifolds, e.g. stably causal and globally hyperbolic spacetimes. These Euler-Lagrange equations for the total mixed scalar curvature (as analog of Einstein-Hilbert action) involve a new kind of Ricci curvature (called the mixed Ricci curvature). In the work, we derive Euler-Lagrange equations of the action for any spacetime, in fact, for a pseudo-Riemannian manifold endowed with a non-degenerate distribution. The obtained equations are presented in the classical form of Einstein field equation with the new Ricci type curvature instead of Ricci curvature
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Garfinkle, David, and Steven G. Harris. "Ricci fall-off in static and stationary, globally hyperbolic, non-singular spacetimes." Classical and Quantum Gravity 14, no. 1 (January 1, 1997): 139–51. http://dx.doi.org/10.1088/0264-9381/14/1/015.

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Dappiaggi, Claudio, Giuseppe Ruzzi, and Ezio Vasselli. "Aharonov–Bohm superselection sectors." Letters in Mathematical Physics 110, no. 12 (October 17, 2020): 3243–78. http://dx.doi.org/10.1007/s11005-020-01335-4.

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AbstractWe show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper, we show that this “topological” quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov–Bohm effect. To confirm these abstract results, we quantize the Dirac field in the presence of a background flat potential and show that the Aharonov–Bohm phase gives an irreducible representation of the fundamental group of the spacetime labelling the charged sectors of the Dirac field. We also show that non-Abelian generalizations of this effect are possible only on spacetimes with a non-Abelian fundamental group.
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Dissertations / Theses on the topic "Non-Globally Hyperbolic Spacetimes"

1

Bullock, David. "Klein-Gordon solutions on non-globally hyperbolic standard static spacetimes." Thesis, University of York, 2011. http://etheses.whiterose.ac.uk/1954/.

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We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a technical condition: ``acceptability") of (some variant of) the Laplace-Beltrami operator defined on test functions in a L^2 space of the static hypersurface. The proof of the existence of this construction completes and extends work originally done by Wald. Further results include the uniqueness of these solutions, their support properties, the construction of the space of solutions and the energy and symplectic form on this space and an analysis of certain symmetries on the space of solutions and of various examples of this method, including the construction of a non-bounded below acceptable self-adjoint extension generating the dynamics.
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2

Bugdayci, Necmi. "Scalar Waves In Spacetimes With Closed Timelike Curves." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12607107/index.pdf.

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The existence and -if exists- the nature of the solutions of the scalar wave equation in spacetimes with closed timelike curves are investigated. The general properties of the solutions on some class of spacetimes are obtained. Global monochromatic solutions of the scalar wave equation are obtained in flat wormholes of dimensions 2+1 and 3+1. The solutions are in the form of infinite series involving cylindirical and spherical wave functions and they are elucidated by the multiple scattering method. Explicit solutions for some limiting cases are illustrated as well. The results of 2+1 dimensions are verified by using numerical methods.
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Book chapters on the topic "Non-Globally Hyperbolic Spacetimes"

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Doboszewski, Juliusz. "Non-uniquely Extendible Maximal Globally Hyperbolic Spacetimes in Classical General Relativity: A Philosophical Survey." In European Studies in Philosophy of Science, 193–212. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55486-0_11.

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