Generating asymptotically plane wave spacetimes

TL;DR

This paper explores solutions to Einstein's equations that describe asymptotically plane wave spacetimes with horizons, finding that pure vacuum solutions lack regular horizons, but extremal solutions with matter can have such horizons.

Contribution

It demonstrates the existence of extremal supergravity solutions with asymptotic plane wave behavior and regular horizons, extending previous vacuum solutions.

Findings

Vacuum solutions with null Killing fields lack regular horizons.

Extremal supergravity solutions can have regular horizons and asymptotic plane wave behavior.

Deformation of M2-brane yields asymptotically plane wave spacetime with horizon.

Abstract

In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line.