paper

On discrete features of the wave equation in singular pp-wave backgrounds

arXiv:0806.3057 · doi:10.1088/1126-6708/2008/09/105

Abstract

We analyze the wave equation in families of pp-wave geometries developing strong localized scale-invariant singularities in certain limits. For both cases of well-localized pp-waves and the so-called null-cosmologies, we observe an intriguing discrete dependence of the existence of a singular limit on the normalization of the pp-wave profile. We also find restrictive matching conditions relating the geometries before and after the singularity (if a singular limit for the solutions of the wave equation with initial conditions specified away from the near-singular region is assumed to exist).

10 pages; v2: references and clarifications added, minor typos corrected

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