Homogeneity and plane-wave limits

TL;DR

This paper investigates the plane-wave limits of homogeneous spacetimes, showing how these limits preserve homogeneity and can be explicitly characterized using Lie algebraic data, with applications demonstrated through examples.

Contribution

It provides a Lie algebraic framework for understanding plane-wave limits of homogeneous spacetimes and examines the behavior of homogeneous structures under these limits.

Findings

Plane-wave limits along homogeneous geodesics remain homogeneous.

Explicit Lie algebraic formulas for the limiting metrics.

Analysis of homogeneous structures under the plane-wave limit.

Abstract

We explore the plane-wave limit of homogeneous spacetimes. For plane-wave limits along homogeneous geodesics the limit is known to be homogeneous and we exhibit the limiting metric in terms of Lie algebraic data. This simplifies many calculations and we illustrate this with several examples. We also investigate the behaviour of (reductive) homogeneous structures under the plane-wave limit.