Symmetries of pp-waves with distributional profile

Abstract

We generalize the classification of (non-vacuum) pp-waves [1] based on the Killing-algebra of the space-time by admitting distributionvalued profile functions. Our approach is based on the analysis of the (infinite-dimensional) group of "normal-form-preserving" diffeomorphisms.

Geodesics for impulsive gravitational waves and the multiplication of distributions

“…However, since we do not want to restrict ourselves to vacuum geometries, we require that the Ricci-tensor is proportional to the tensor square of p a . ¿From these requirements one shows [8,9] that the metric may be written as…”

Generalized symmetries of impulsive gravitational waves

“…In a previous paper [1] the authors considered symmetries of impulsive planefronted waves with parallel rays. The motivation for this study was the failure of the classical work by Jordan, Ehlers and Kundt (JEK) [2] for wave profiles which are generalized functions [3].…”

“…The motivation for this study was the failure of the classical work by Jordan, Ehlers and Kundt (JEK) [2] for wave profiles which are generalized functions [3]. In order to solve this problem a new systematic approach for the classification of general pp-waves was presented [1], which was in the following applied to the simplest class of impulsive spacetimes, where the wave is concentrated on a single null hyperplane. It was shown that even vacuum spacetimes within this class contain new symmetries which have no non-impulsive analogue.…”

The use of generalized functions and distributions in general relativity

“…Furthermore it has also been possible to define generalised functions taking values in a manifold and this allows one to talk about generalised geodesics and generalised symmetries (see e.g. [2]) of a spacetime. Unfortunately due to lack of space we have had to omit from this review both this latter topic and the topic of impulsive pp-waves and ultrarelativistic black holes with non-vanishing cosmological constant (see e.g.…”