Non-Einstein geometries in Chiral Gravity

TL;DR

This paper explores non-Einstein solutions in Chiral Gravity, revealing their singularities, horizons, and closed timelike curves, thus expanding understanding of the theory's solution space.

Contribution

It provides the first exact non-linear non-Einstein solution in Chiral Gravity and analyzes its physical properties and implications.

Findings

Non-Einstein solutions can have interior curvature singularities.

Back-reaction creates horizons and geodesic repulsion.

Solutions include closed timelike curves.

Abstract

We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on non-Einstein metrics. A class of such solutions admits curvature singularities in the interior which are reflected as singularities or infinite bulk energy of the corresponding linear solutions. A non-linear solution is found exactly. The back-reaction induces a repulsion of geodesics and a shielding of the singularity by an event horizon but also introduces closed timelike curves.