Testing a stability conjecture with plane-wave Cauchy horizons

Abstract

Plane-wave Cauchy horizons serve as an important testing ground for a previously developed Cauchy horizon stability conjecture. The conjecture uses test fields to predict the stability of Cauchy horizons in general relativistic spacetimes. Three cases are considered: single plane waves with (a) aligned test fields and (b) colliding test fields; and (c) non-singular interaction regions in colliding-wave spacetimes. A restricted form of the stability conjecture is proven for case (a). The conjecture is shown to agree with arbitrary exact back-reaction solutions in this case, as long as no Weyl-tensor singularities are introduced on an initial Cauchy surface. Four examples of case (b) are analysed; in three the conjecture agrees with exact back-reaction solutions, and in the fourth the conjecture correctly indicates instability, but misjudges the type of singularity formed. A possible reason for the disagreement is discussed. Two examples of case (c) are analysed, in which test null dust is added to the interaction regions of a colliding electromagnetic spacetime (Bell-Szekeres) and a colliding gravitational wave spacetime (Chandrasekhar-Xanthopoulos). The conjecture is shown to agree with known exact back-reaction solutions.