Supergravity on an Atiyah-Hitchin Base

TL;DR

This paper constructs five-dimensional supergravity solutions on an Atiyah-Hitchin base, revealing that most solutions contain a velocity of light surface that shields singularities, preventing causality violations outside this surface.

Contribution

It introduces new supergravity solutions on an Atiyah-Hitchin base and analyzes their causal structure, showing how velocity of light surfaces can hide singularities.

Findings

Most solutions have a velocity of light surface shielding singularities.

Solutions outside the surface are causally well-behaved and geodesically complete.

Some parameter choices lead to naked singularities without such shielding.

Abstract

We construct solutions to five dimensional minimal supergravity using an Atiyah-Hitchin base space. In examining the structure of solutions we show that they generically contain a singularity either on the Atiyah-Hitchin bolt or at larger radius where there is a singular solitonic boundary. However for most points in parameter space the solution exhibits a velocity of light surface (analogous to what appears in a Goedel space-time) that shields the singularity. For these solutions, all closed time-like curves are causally disconnected from the rest of the space-time in that they exist within the velocity of light surface, which null geodesics are unable to cross. The singularities in these solutions are thus found to be hidden behind the velocity of light surface and so are not naked despite the lack of an event horizon. Outside of this surface the space-time is geodesically complete, asymptotically flat and can be arranged so as not to contain closed time-like curves at infinity. The rest of parameter space simply yields solutions with naked singularities.