Critical gravity in the Chern-Simons modified gravity

TL;DR

This paper analyzes perturbations of Chern-Simons modified gravity around AdS4 spacetime to identify conditions for critical gravity, revealing a specific massive solution and its behavior at the critical point.

Contribution

It provides the first explicit perturbation analysis of Chern-Simons modified gravity around AdS4, identifying the critical point where linear excitations vanish.

Findings

Derived the mass squared of the AdS wave solution as a function of parameters.

Identified the critical coupling where the massive mode becomes massless.

Showed the solution takes a log-form at the critical point.

Abstract

We perform the perturbation analysis of the Chern-Simons modified gravity around the AdS$_4$ spacetimes (its curvature radius $\ell$) to obtain the critical gravity. In general, we could not obtain an explicit form of perturbed Einstein equation which shows a massive graviton propagation clearly, but for the Kerr-Schild perturbation and Chern-Simons coupling $\theta=kx/y$, we find the AdS wave as a single massive solution to the perturbed Einstein equation. Its mass squared is given by $M^2=[-9+(2\ell^2/k-1)^2]/4\ell^2$. At the critical point of $M^2=0(k=\ell^2/2)$, the solution takes the log-form and the linearized excitation energies vanish.