Asymptotically Plane Wave Spacetimes and their Actions

TL;DR

This paper defines asymptotically plane wave spacetimes in vacuum gravity, constructs a finite action principle for them, and establishes well-posedness of the variational principle under these conditions.

Contribution

It introduces a new definition of asymptotically plane wave spacetimes and develops a corresponding finite action principle for vacuum gravity.

Findings

The action is finite on-shell for these spacetimes.

The variational principle is well-defined under the new falloff conditions.

Connections to previously known solutions are discussed.

Abstract

We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave falloff conditions.