Collisions of Shock Waves in General Relativity

TL;DR

This paper analyzes the collision of gravitational and electromagnetic shock waves in general relativity, revealing conditions under which the interaction region forms specific homogeneous solutions with a cosmological constant.

Contribution

It introduces a detailed description of shock wave collisions, including electromagnetic components, and identifies conditions leading to particular homogeneous space-times post-collision.

Findings

Collision of shock waves can produce a cosmological constant in the interaction region.

Specific algebraic relations between wave parameters determine the resulting space-time.

The study extends understanding of Einstein-Maxwell solutions with shock wave interactions.

Abstract

We show that the Nariai-Bertotti Petrov type D, homogeneous solution of Einstein's vacuum field equations with a cosmological constant describes the space-time in the interaction region following the head-on collision of two homogeneous, plane gravitational shock waves each initially traveling in a vacuum containing no cosmological constant. A shock wave in this context has a step function profile in contrast to an impulsive wave which has a delta function profile. Following the collision two light-like signals, each composed of a plane, homogeneous light-like shell of matter and a plane, homogeneous impulsive gravitational wave, travel away from each other and a cosmological constant is generated in the interaction region. Furthermore a plane, light-like signal consisting of an electromagnetic shock wave accompanying a gravitational shock wave is described with the help of two real parameters, one for each wave. The head-on collision of two such light-like signals is examined and we show that if a simple algebraic relation is satisfied between the two pairs of parameters associated with each incoming light-like signal then the space-time in the interaction region following the collision is a Bertotti space-time which is a homogeneous solution of the vacuum Einstein-Maxwell field equations with a cosmological constant.