Critical gravity in the Chern-Simons modified gravity

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.

13 pages, 1 figure, version to appear in EPJC

References in corpus (8)

• Critical Gravity in Four Dimensions
• Critical Points of D-Dimensional Extended Gravities
• AdS Waves as Exact Solutions to Quadratic Gravity
• D-Dimensional Log Gravity
• Modes of Log Gravity
• Ghosts of Critical Gravity
• Chern-Simons Modified General Relativity: Conserved charges
• Deeper discussion of Schrödinger invariant and Logarithmic sectors of higher-curvature gravity

Cited by in corpus (5)

• AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
• Noncritical Einstein-Weyl Gravity and the AdS/CFT Correspondence
• Linearized Modes in Extended and Critical Gravities
• Massive gravitational waves in Chern-Simons modified gravity
• Tricritical gravity waves in the four-dimensional generalized massive gravity