CAUCHY SURFACE

2006 ◽  
Vol c ◽  
Keyword(s):  
Cauchy Surface

An R 4 spacetime with a Cauchy surface which is not R 3

1987 ◽  
Vol 4 (1) ◽  
pp. 53-60 ◽  
Author(s):  
R P A C Newman ◽  
C J S Clark
Keyword(s):  
Cauchy Surface

scholarly journals Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime

2017 ◽  
Vol 29 (04) ◽  
pp. 1750014 ◽  
Author(s):  
Michał Wrochna ◽  
Jochen Zahn
Keyword(s):  
Phase Space ◽  
Cauchy Surface ◽  
Gauge Field Theories ◽  
Subsidiary Condition ◽  
Yang Mills ◽  
Special Cases ◽  
Hadamard States ◽  
Hyperbolic Spacetimes ◽  
Definition Of ◽  
Classical Phase Space

We investigate linearized gauge theories on globally hyperbolic spacetimes in the BRST formalism. A consistent definition of the classical phase space and of its Cauchy surface analogue is proposed. We prove that it is isomorphic to the phase space in the ‘subsidiary condition’ approach of Hack and Schenkel in the case of Maxwell, Yang–Mills, and Rarita–Schwinger fields. Defining Hadamard states in the BRST formalism in a standard way, their existence in the Maxwell and Yang–Mills case is concluded from known results in the subsidiary condition (or Gupta–Bleuler) formalism. Within our framework, we also formulate criteria for non-degeneracy of the phase space in terms of BRST cohomology and discuss special cases. These include an example in the Yang–Mills case, where degeneracy is not related to a non-trivial topology of the Cauchy surface.

HADAMARD STATES, ADIABATIC VACUA AND THE CONSTRUCTION OF PHYSICAL STATES FOR SCALAR QUANTUM FIELDS ON CURVED SPACETIME

1996 ◽  
Vol 08 (08) ◽  
pp. 1091-1159 ◽  
Author(s):  
WOLFGANG JUNKER
Keyword(s):  
Pseudodifferential Operators ◽  
Cauchy Surface ◽  
Positive Energy ◽  
Hyperbolic Spacetime ◽  
Vacuum States ◽  
Mathematical Review ◽  
Scalar Quantum ◽  
Klein Gordon ◽  
Hadamard States ◽  
Adiabatic Vacuum

Quasifree states of a linear Klein-Gordon quantum field on globally hyperbolic spacetime manifolds are considered. After a short mathematical review techniques from the theory of pseudodifferential operators and wavefront sets on manifolds are used to develop a criterion for a state to be an Hadamard state. It is proven that ground- and KMS-states on certain static spacetimes and adiabatic vacuum states on Robertson-Walker spaces are Hadamard states. A counterexample is given which shows that the idea of instantaneous positive energy states w.r.t. a Cauchy surface does in general not yield physical states. Finally, the problem of constructing Hadamard states on arbitrary curved spacetimes is solved in principle.

QUANTIZED ELECTROMAGNETIC FIELD ON A MANIFOLD

1992 ◽  
Vol 04 (02) ◽  
pp. 223-233 ◽  
Author(s):  
J. DIMOCK
Keyword(s):  
Electromagnetic Field ◽  
Lorentzian Manifold ◽  
Cauchy Surface ◽  
Globally Hyperbolic ◽  
Quantized Electromagnetic Field

We develop the quantization of the electromagnetic field on an arbitrary globally hyperbolic Lorentzian manifold with a compact Cauchy surface.

scholarly journals Information loss paradox revisited: Farewell firewall?

2020 ◽  
Vol 29 (14) ◽  
pp. 2043019
Author(s):  
Wen-Cong Gan ◽  
Fu-Wen Shu
Keyword(s):  
Hawking Radiation ◽  
Pure State ◽  
Cauchy Surface ◽  
Information Loss ◽  
Total System ◽  
Simple Argument ◽  
Unitary Evolution ◽  
Information Loss Paradox ◽  
Flat Spacetime ◽  
Gravity Effects

Unitary evolution makes pure state on one Cauchy surface evolve to pure state on another Cauchy surface. Outgoing Hawking radiation is the only subsystem on the late Cauchy surface. The requirement that Hawking radiation should be pure amounts to requiring purity of the subsystem when the total system is pure. We will see that this requirement will lead to firewall even in flat spacetime, and thus is invalid. Information is either stored in the entanglement between field modes inside black hole and the outgoing modes or stored in correlation between geometry and Hawking radiation when singularity is resolved by quantum gravity effects. We will give a simple argument that even in semi-classical regime, information is (at least partly) stored in correlation between geometry and Hawking radiation.

Curvature, causality and completeness in space-times with causally complete spacelike slices

1986 ◽  
Vol 99 (2) ◽  
pp. 367-375 ◽  
Author(s):  
Gregory J. Galloway
Keyword(s):  
Initial Data ◽  
Minkowski Space ◽  
Cauchy Surface ◽  
Space Time ◽  
Finiteness Condition ◽  
Cauchy Horizon ◽  
Asymptotically Flat ◽  
The Future

Let S be a spacelike slice (defined formally in Section 2) in a space-time M. We will say that S is future causally complete in M if for each p ε J+(S) the closure in S of the set J-(p) ∩ S is compact. Define past causal completeness time-dually. Then S is causally complete if it is both future and past causally complete. A compact spacelike slice is necessarily causally complete, as is any Cauchy surface, but the concept of causal completeness is much broader than either of these two conditions. For example the slices t = const. ≠ 0 in the space-time obtained by removing the origin from Minkowski space are causally complete, although they are neither Cauchy nor compact. The slice t = 0 in the previous example and the hyperboloid in Minkowski space (where (t, x1, …, xn) are standard inertial coordinates) are examples of slices which are not causally complete. Physically speaking, an edgeless slice S is future causally complete if the information from S which reaches a point in the future of S comes from a finite nonsingular region in S. The Maximal Reissner-Nordstrom space-time is a well-known example in which this finiteness condition is not fulfilled by any of its asymptotically flat partial Cauchy surfaces. Indeed for any such partial Cauchy surface S, J-(p) ∩ S is non-compact for any p ε H+(S). However, as has been discussed in the literature (e.g. [17], p. 625 f), it is believed that the Cauchy horizon in this situation is unstable with respect to perturbations of the initial data on S.

The Cauchy surface wave problem from the viewpoint of a VOF method

2005 ◽  
Vol 39 (2) ◽  
pp. 141-152 ◽  
Author(s):  
Stefan aus der Wiesche
Keyword(s):  
Surface Wave ◽  
Cauchy Surface ◽  
Vof Method ◽  
Wave Problem

scholarly journals Some results on Cauchy surface criteria in Lorentzian geometry

1985 ◽  
Vol 29 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Gregory J. Galloway
Keyword(s):  
Cauchy Surface ◽  
Lorentzian Geometry

Conformal deformations, Ricci curvature and energy conditions on globally hyperbolic spacetimes

1978 ◽  
Vol 84 (1) ◽  
pp. 159-175 ◽  
Author(s):  
John K. Beem ◽  
Paul E. Ehrlich
Keyword(s):  
Ricci Curvature ◽  
Energy Condition ◽  
Cauchy Surface ◽  
Energy Conditions ◽  
Curvature Condition ◽  
Globally Hyperbolic ◽  
Globally Hyperbolic Spacetimes ◽  
Dimension 2 ◽  
Hyperbolic Spacetimes ◽  
Conformal Deformations

AbstractWe consider globally hyperbolic spacetimes (M, g) of dimension ≥ 3 satisfying the curvature condition Ric (g) (v, v) ≥ 0 for all non-spacelike tangent vectors v in TM. This curvature condition arises naturally as an energy condition in cosmology. Suppose (M, g) admits a smooth globally hyperbolic time function h: M → such that for some t0, the Cauchy surface h−1(t0) satisfies the strict curvature condition Ric (g) (v, v) > 0 for all non-spacelike v attached to h−1(t0). Then M admits a metric g′ conformal to g satisfying the strict curvature condition Ric (g′) (v, v) > 0 for all non-spacelike v in TM. If the curvature and strict curvature conditions are restricted to null vectors, the analogous result may be obtained. Similar results may also be obtained for the scalar curvature in dimension ≥ 2 and for non-positive Ricci curvature.

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