Singularities in Hyperscaling Violating Spacetimes

TL;DR

This paper investigates hyperscaling violating spacetimes, revealing most have singularities either naked or null, with a rare family avoiding these issues but requiring exotic matter with negative energy density.

Contribution

It extends the analysis of Lifshitz singularities to hyperscaling violating spacetimes and identifies conditions under which singularities can be avoided.

Findings

Most hyperscaling violating spacetimes have naked or null singularities.

A one-parameter family avoids singularities but involves exotic matter.

Exotic matter with negative energy density is necessary for singularity avoidance.

Abstract

We examine spacetimes which generalize Lifshitz scaling to allow hyperscaling violation invariance (i.e. a constant conformal transformation) for the types of singularities frequently found in the Lifshitz case. We find that most of these spacetimes suffer either from a traditional naked curvature singularity or a null curvature singularity robust against stringy higher derivative corrections. We do find a one-parameter family that evades these issues but this family requires exotic matter, in particular involving a negative energy density that may not be interpreted as due to a cosmological constant.