Spherical shock waves in general relativity

Details Spherical shock waves in general relativity Spherical shock waves in general relativity

Nov 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..44.3164n&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 44, Issue 10, 15 November 1991, pp.3164-3168

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Scientific paper

We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-N vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-N Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the C0-form of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.

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