Eur. Phys. J. C (2011) 71: 1796
https://doi.org/10.1140/epjc/s10052-011-1796-x

Regular Article - Theoretical Physics

Critical gravity in the Chern–Simons modified gravity

¹ Center for Quantum Space-time, Sogang University, Seoul, 121-742, Korea
² Institute of Basic Sciences and School of Computer Aided Science, Inje University, Gimhae, 621-749, Korea

^* e-mail: ysmyung@inje.ac.kr

Received: 18 October 2011
Revised: 25 October 2011
Published online: 10 November 2011

Abstract

We perform the perturbation analysis of the Chern–Simons modified gravity around the AdS₄ spacetime (its curvature radius ℓ) 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 θ=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+(2ℓ ²/k−1)²]/4ℓ ². At the critical point of M ²=0 (k=ℓ ²/2), the solution takes the log-form and the linearized excitation energies vanish.