Eur. Phys. J. C (2013) 73: 2308
https://doi.org/10.1140/epjc/s10052-013-2308-y

Regular Article - Theoretical Physics

Tricritical gravity waves in the four-dimensional generalized massive 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: 19 September 2012
Published online: 9 February 2013

Abstract

We construct a generalized massive gravity by combining quadratic curvature gravity with the Chern–Simons term in four dimensions. This may be a candidate for the parity-odd tricritical gravity theory. Considering the AdS₄ vacuum solution, we derive the linearized Einstein equation, which is not similar to that of the three dimensional (3D) generalized massive gravity. When a perturbed metric tensor is chosen to be the Kerr–Schild form, the linearized equation reduces to a single massive scalar equation. At the tricritical points where two masses are equal to −1 and 2, we obtain a log-square wave solution to the massive scalar equation. This is compared to 3D tricritical generalized massive gravity, whose dual is a rank-3 logarithmic conformal field theory.