On Horizons and Plane Waves

TL;DR

This paper explores the conditions under which horizons can exist in supergravity solutions asymptotic to IIB plane waves, showing that null Killing vectors prevent horizon formation and proposing ways to circumvent this limitation.

Contribution

It demonstrates that null Killing vectors hinder horizon formation in such backgrounds and suggests removing them to achieve horizons, providing a perturbative approach to this idea.

Findings

Null Killing vectors prevent horizon formation in these backgrounds.

Non-extremal solutions lead to naked singularities.

Removing the null Killing vector may allow horizons to form.

Abstract

We investigate the possibility of having an event horizon within several classes of metrics that asymptote to the maximally supersymmetric IIB plane wave. We show that the presence of a null Killing vector (not necessarily covariantly constant) implies an effective separation of the Einstein equations into a standard and a wave component. This feature may be used to generate new supergravity solutions asymptotic to the maximally supersymmetric IIB plane wave, starting from standard seed solutions such as branes or intersecting branes in flat space. We find that in many cases it is possible to preserve the extremal horizon of the seed solution. On the other hand, non-extremal deformations of the plane wave solution result in naked singularities. More generally, we prove a no-go theorem against the existence of horizons for backgrounds with a null Killing vector and which contain at most null matter fields. Further attempts at turning on a nonzero Hawking temperature by introducing additional matter have proven unsuccessful. This suggests that one must remove the null Killing vector in order to obtain a horizon. We provide a perturbative argument indicating that this is in fact possible.