Tricritical gravity waves in the four-dimensional generalized massive gravity

TL;DR

This paper constructs a four-dimensional generalized massive gravity model combining quadratic curvature and Chern-Simons terms, analyzing its linearized equations and solutions at tricritical points, with potential duality to logarithmic conformal field theories.

Contribution

It introduces a novel 4D tricritical gravity model with explicit solutions and compares its properties to known 3D models, expanding the understanding of higher-dimensional gravity theories.

Findings

Derived linearized Einstein equations for the model.

Found log-square wave solutions at tricritical points.

Identified potential duality with logarithmic conformal field theories.

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 AdS$_4$ 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 the 3D tricritical generalized massive gravity whose dual is a rank-3 logarithmic conformal field theory.