The stability of Killing-Cauchy horizons in colliding plane wave space-times

It is confirmed rigorously that the Killing-Cauchy horizons, which sometimes occur in space-times representing the collision and subsequent interaction of plane gravitational waves in a Minkowski background, are unstable with respect to bounded perturbations of the initial waves, at least for the case in which the initial waves have constant aligned polarizations.Comment: 8 pages. To appear in Gen. Rel. Gra

Colliding Axion-Dilaton Plane Waves from Black Holes

The colliding plane wave metric discovered by Ferrari and Iba\~{n}ez to be locally isometric to the interior of a Schwarzschild black hole is extended to the case of general axion-dilaton black holes. Because the transformation maps either black hole horizon to the focal plane of the colliding waves, this entire class of colliding plane wave spacetimes only suffers from the formation of spacetime singularities in the limits where the inner horizon itself is singular, which occur in the Schwarzschild and dilaton black hole limits. The supersymmetric limit corresponding to the extreme axion-dilaton black hole yields the Bertotti-Robinson metric with the axion and dilaton fields flowing to fixed constant values. The maximal analytic extension of this metric across the Cauchy horizon yields a spacetime in which two sandwich waves in a cylindrical universe collide to produce a semi-infinite chain of Reissner-Nordstrom-like wormholes. The focussing of particle and string geodesics in this spacetime is explored.Comment: 19 pages, 6 figure

Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes

The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved spacetime are the canonical commutation relations, imposed on the field operators evaluated at a global Cauchy surface. In the algebraic formulation of linear quantum field theory, the canonical commutation relations are restated in terms of a well-defined symplectic structure on the space of smooth solutions, and the local field algebra is constructed as the Weyl algebra associated to this symplectic vector space. When spacetime is not globally hyperbolic, e.g. when it contains naked singularities or closed timelike curves, a global Cauchy surface does not exist, and there is no obvious way to formulate the canonical commutation relations, hence no obvious way to construct the field algebra. In a paper submitted elsewhere, we report on a generalization of the algebraic framework for quantum field theory to arbitrary topological spaces which do not necessarily have a spacetime metric defined on them at the outset. Taking this generalization as a starting point, in this paper we give a prescription for constructing the field algebra of a (massless or massive) Klein-Gordon field on an arbitrary background spacetime. When spacetime is globally hyperbolic, the theory defined by our construction coincides with the ordinary Klein-Gordon field theory on aComment: 21 pages, UCSBTH-92-4

Focusing and the Holographic Hypothesis

The ``screen mapping" introduced by Susskind to implement 't Hooft's holographic hypothesis is studied. For a single screen time, there are an infinite number of images of a black hole event horizon, almost all of which have smaller area on the screen than the horizon area. This is consistent with the focusing equation because of the existence of focal points. However, the {\it boundary} of the past (or future) of the screen obeys the area theorem, and so always gives an expanding map to the screen, as required by the holographic hypothesis. These considerations are illustrated with several axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi

The Effect of Sources on the Inner Horizon of Black Holes

Single pulse of null dust and colliding null dusts both transform a regular horizon into a space-like singularity in the space of colliding waves. The local isometry between such space-times and black holes extrapolates these results to the realm of black holes. However, inclusion of particular scalar fields instead of null dusts creates null singularities rather than space-like ones on the inner horizons of black holes.Comment: Final version to appear in PR

The Near-Linear Regime of Gravitational Waves in Numerical Relativity

We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the amplitude of the wave is low enough that one expects the geometric deviation from flat spacetime to be negligible, but nevertheless where nonlinearities can excite unstable modes of the Einstein evolution equations causing the metric functions to evolve out of control. The implications of this for numerical relativity are discussed.Comment: 10 pages, 2 postscript figures, revised tex

No time machines in classical general relativity

Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are defined to be causality-violating regions created by human beings (as opposed to those appearing spontaneously).Comment: A corrigendum (to be published in CQG) has been added to correct an important mistake in the definition of localit

Quantum field theory and time machines

We analyze the "F-locality condition" (proposed by Kay to be a mathematical implementation of a philosophical bias related to the equivalence principle, we call it the "GH-equivalence principle"), which is often used to build a generalization of quantum field theory to non-globally hyperbolic spacetimes. In particular we argue that the theorem proved by Kay, Radzikowski, and Wald to the effect that time machines with compactly generated Cauchy horizons are incompatible with the F-locality condition actually does not support the "chronology protection conjecture", but rather testifies that the F-locality condition must be modified or abandoned. We also show that this condition imposes a severe restriction on the geometry of the world (it is just this restriction that comes into conflict with the existence of a time machine), which does not follow from the above mentioned philosophical bias. So, one need not sacrifice the GH-equivalence principle to "emend" the F-locality condition. As an example we consider a particular modification, the "MF-locality condition". The theory obtained by replacing the F-locality condition with the MF-locality condition possesses a few attractive features. One of them is that it is consistent with both locality and the existence of time machines.Comment: Revtex, 14 pages, 1 .ps figure. To appear in Phys. Rev. D More detailed discussion is given on the MF-locality condition. Minor corrections in terminolog

Neutrino current in a gravitational plane wave collision background

The behaviour of a massless Dirac field on a general spacetime background representing two colliding gravitational plane waves is discussed in the Newman-Penrose formalism. The geometrical properties of the neutrino current are analysed and explicit results are given for the special Ferrari-Ibanez solution.Comment: 17 pages, 6 Postscript figures, accepted by International Journal of Modern Physics