Impulsive spherical gravitational waves

TL;DR

This paper develops a spinor formalism to derive exact solutions for impulsive spherical gravitational waves, generalizing Penrose's warp identification method and including cases with accelerated vertices.

Contribution

It introduces a new spinor-based approach to construct impulsive spherical gravitational wave metrics, simplifying derivations and extending solutions to accelerated null cone vertices.

Findings

Derived a family of impulsive spherical gravitational wave metrics

Presented a new solution with an accelerated vertex

Simplified the derivation process using spinor techniques

Abstract

Penrose's identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the 2-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These solutions of the Einstein vacuum field equations are obtained by cutting Minkowski space into two pieces along a null cone and re-identifying them with warp which is given by an arbitrary non-linear holomorphic transformation. Using 2-component spinor techniques we construct a new metric describing an impulsive spherical gravitational wave where the vertex of the null cone lies on a world-line with constant acceleration.