Exact Parallel Waves in General Relativity

TL;DR

This paper reviews the fundamental concepts and recent developments in the study of parallel wave spacetimes in general relativity, emphasizing their geometric properties, coordinate systems, and causality aspects.

Contribution

It provides a comprehensive overview of definitions, classical results, and recent progress on causality and the Ehlers-Kundt conjecture in parallel wave spacetimes.

Findings

Existence of null coordinates in wave spacetimes

Construction of Penrose limits for these geometries

Progress on the Ehlers-Kundt conjecture

Abstract

We conduct a review of the basic definitions and the principal results in the study of wavelike spacetimes, that is spacetimes whose metric models massless radiation moving at the speed of light, focusing in particular on those geometries with parallel rays. In particular, we motivate and connect their various definitions, outline their coordinate descriptions and present some classical results in their study in a language more accessible to modern readers, including the existence of "null coordinates" and the construction of Penrose limits. We also present a thorough summary of recent work on causality in pp-waves, and describe progress in addressing an open question in the field - the Ehlers-Kundt conjecture.