Topologically Massive Gravity and Ricci-Cotton Flow

TL;DR

This paper investigates the decay processes of Anti-de Sitter and Warped Anti-de Sitter spaces in Topologically Massive Gravity using Ricci-Cotton flow, revealing how solutions transition depending on the Chern-Simons coupling strength.

Contribution

It introduces Ricci-Cotton flow as a tool to analyze vacuum solution decay in TMG and explores the parameter-dependent flow directions between AdS and warped AdS spaces.

Findings

AdS flows to warped AdS at small Chern-Simons coupling.

Warped AdS flows to AdS at large Chern-Simons coupling.

Explicit minisuperspace models demonstrate these flows.

Abstract

We consider Topologically Massive Gravity (TMG), which is three dimensional general relativity with a cosmological constant and a gravitational Chern-Simons term. When the cosmological constant is negative the theory has two potential vacuum solutions: Anti-de Sitter space and Warped Anti-de Sitter space. The theory also contains a massive graviton state which renders these solutions unstable for certain values of the parameters and boundary conditions. We study the decay of these solutions due to the condensation of the massive graviton mode using Ricci-Cotton flow, which is the appropriate generalization of Ricci flow to TMG. When the Chern-Simons coupling is small the AdS solution flows to warped AdS by the condensation of the massive graviton mode. When the coupling is large the situation is reversed, and warped AdS flows to AdS. Minisuperspace models are constructed where these flows are studied explicitly.