Penrose limits of inhomogeneous space-times, their diagonalizability and twistors

TL;DR

This paper investigates Penrose limits in inhomogeneous space-times with two spacelike symmetries, analyzing their diagonalizability and solutions to the twistor equation, relevant for cosmological and wave phenomena.

Contribution

It extends the analysis of Penrose limits to inhomogeneous cosmologies and wave interactions, exploring conditions for diagonalizability and twistor solutions in these complex backgrounds.

Findings

Conditions for diagonal Penrose limits are identified.

Solutions to the twistor equation are constructed in these limits.

Applications to inhomogeneous cosmologies and wave interactions are discussed.

Abstract

Penrose limits are considered in space-times admitting two abelian, space-like Killing vectors in vacuum as well as in the presence of an electromagnetic field. This type of space-times describe inhomogeneous cosmologies as well as colliding plane gravitational and electromagnetic waves. Following the work of Tod [1] the conditions for diagonal Penrose limits are investigated in these backgrounds. The twistor equation is considered in these space-times and solutions given in the Penrose limit.