Instability of Killing-Cauchy horizons in plane-symmetric spacetimes

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Abstract
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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