scholarly journals Cauchy and uniform temporal functions of globally hyperbolic cone fields

2020 ◽  
Vol 148 (11) ◽  
pp. 4951-4966
Author(s):  
Patrick Bernard ◽  
Stefan Suhr
Keyword(s):  
Globally Hyperbolic ◽  
Cone Fields

scholarly journals The globally hyperbolic metric splitting for non-smooth wave-type space-times

2014 ◽  
Vol 420 (1) ◽  
pp. 348-363 ◽  
Author(s):  
Günther Hörmann ◽  
Clemens Sämann
Keyword(s):  
Hyperbolic Metric ◽  
Wave Type ◽  
Type Space ◽  
Globally Hyperbolic

scholarly journals Cone-fields without constant orbit core dimension

2012 ◽  
Vol 32 (10) ◽  
pp. 3651-3664 ◽  
Author(s):  
Tomasz Kułaga ◽  
Jacek Tabor ◽  
Łukasz Struski
Keyword(s):  
Cone Fields

scholarly journals Quantum field theory on certain non-globally hyperbolic spacetimes

1996 ◽  
Vol 13 (1) ◽  
pp. 51-61 ◽  
Author(s):  
C J Fewster ◽  
A Higuchi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Globally Hyperbolic ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes

scholarly journals Dynamics in non-globally-hyperbolic static spacetimes: II. General analysis of prescriptions for dynamics

2003 ◽  
Vol 20 (16) ◽  
pp. 3815-3826 ◽  
Author(s):  
Akihiro Ishibashi ◽  
Robert M Wald
Keyword(s):  
General Analysis ◽  
Globally Hyperbolic

scholarly journals Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds

2017 ◽  
Vol 188 (1) ◽  
pp. 63-101 ◽  
Author(s):  
Olivier Glorieux
Keyword(s):  
Closed Geodesics ◽  
Globally Hyperbolic

scholarly journals RECOVERY OF ZEROTH ORDER COEFFICIENTS IN NON-LINEAR WAVE EQUATIONS

2020 ◽  
pp. 1-27
Author(s):  
Ali Feizmohammadi ◽  
Lauri Oksanen
Keyword(s):  
Wave Equations ◽  
Model Problem ◽  
Wave Interaction ◽  
Lorentzian Manifold ◽  
Gaussian Beams ◽  
Linear Wave ◽  
Lorentzian Manifolds ◽  
Solution Map ◽  
Globally Hyperbolic ◽  
Linear Wave Equations

This paper is concerned with the resolution of an inverse problem related to the recovery of a function $V$ from the source to solution map of the semi-linear equation $(\Box _{g}+V)u+u^{3}=0$ on a globally hyperbolic Lorentzian manifold $({\mathcal{M}},g)$ . We first study the simpler model problem, where $({\mathcal{M}},g)$ is the Minkowski space, and prove the unique recovery of $V$ through the use of geometric optics and a three-fold wave interaction arising from the cubic non-linearity. Subsequently, the result is generalized to globally hyperbolic Lorentzian manifolds by using Gaussian beams.

Light-cone fields and particles

2011 ◽  
pp. 166-186
Author(s):  
Barton Zwiebach
Keyword(s):  
Light Cone ◽  
Cone Fields

scholarly journals Globally Hyperbolic Regularization of Grad's Moment System

2013 ◽  
Vol 67 (3) ◽  
pp. 464-518 ◽  
Author(s):  
Zhenning Cai ◽  
Yuwei Fan ◽  
Ruo Li
Keyword(s):  
Globally Hyperbolic ◽  
Moment System

scholarly journals HOMOTOPY OF POSETS, NET-COHOMOLOGY AND SUPERSELECTION SECTORS IN GLOBALLY HYPERBOLIC SPACE-TIMES

2005 ◽  
Vol 17 (09) ◽  
pp. 1021-1070 ◽  
Author(s):  
GIUSEPPE RUZZI
Keyword(s):  
Hyperbolic Space ◽  
Space Time ◽  
Fundamental Groups ◽  
Mathematical Framework ◽  
Permutation Symmetry ◽  
Index Set ◽  
Globally Hyperbolic ◽  
Underlying Space ◽  
Local Observables ◽  
Suitable Change

We study sharply localized sectors, known as sectors of DHR-type, of a net of local observables, in arbitrary globally hyperbolic space-times with dimension ≥ 3. We show that these sectors define, as it happens in Minkowski space, a C*-category in which the charge structure manifests itself by the existence of a tensor product, a permutation symmetry and a conjugation. The mathematical framework is that of the net-cohomology of posets according to J. E. Roberts. The net of local observables is indexed by a poset formed by a basis for the topology of the space-time ordered under inclusion. The category of sectors, is equivalent to the category of 1-cocycles of the poset with values in the net. We succeed in analyzing the structure of this category because we show how topological properties of the space-time are encoded in the poset used as index set: the first homotopy group of a poset is introduced and it is shown that the fundamental group of the poset and one of the underlying space-time are isomorphic; any 1-cocycle defines a unitary representation of these fundamental groups. Another important result is the invariance of the net-cohomology under a suitable change of index set of the net.

scholarly journals On solutions to the wave equation on a non-globally hyperbolic manifold

2009 ◽  
Vol 265 (1) ◽  
pp. 262-275 ◽  
Author(s):  
I. V. Volovich ◽  
O. V. Groshev ◽  
N. A. Gusev ◽  
E. A. Kuryanovich
Keyword(s):  
Wave Equation ◽  
Hyperbolic Manifold ◽  
Globally Hyperbolic
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