Instability of Killing-Cauchy horizons in plane-symmetric spacetimes

Details Instability of Killing-Cauchy horizons in plane-symmetric spacetimes Instability of Killing-Cauchy horizons in plane-symmetric spacetimes

Sep 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvd..36.1662y&link_type=abstract

Physical Review D (Particles and Fields), Volume 36, Issue 6, 15 September 1987, pp.1662-1672

Physics

33

Fundamental Problems And General Formalism

Scientific paper

It is well known that when plane-symmetric gravitational waves collide, they produce singularities. Presently known exact solutions representing such collisions fall into two classes: those in which the singularities are spacelike, and those in which timelike singularities appear preceded by a Killing-Cauchy horizon. This paper shows that Killing-Cauchy horizons in plane-symmetric spacetimes are unstable against plane-symmetric perturbations and thence argues that generic spacetimes representing colliding plane waves are likely to have spacelike singularities without Killing-Cauchy horizons. More specifically, this paper gives an explicit definition of Killing-Cauchy horizons in plane-symmetric spacetimes and classifies these horizons into two types: those which are smooth surfaces, called ``type I,'' and those which are singular, called ``type II.'' It is then shown that type-I horizons are unstable with respect to any generic, plane-symmetric perturbation data posed on a suitable initial null boundary and evolved with arbitrarily nonlinear field equations satisfying some very general requirements; linearized gravitational perturbations constitute a special case of this instability. Horizons of type II are shown to be unstable with respect to generic, plane-symmetric perturbations satisfying linear evolution equations; a special case again is linearized gravitational perturbations.

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