Critical gravity on AdS2 spacetimes

Abstract

We study the critical gravity in two dimensional AdS (AdS${}_2$) spacetimes, which was obtained from the cosmological topologically massive gravity (TMG${}_{\Lambda }$) in three dimensions by using the Kaluza-Klein dimensional reduction. We perform the perturbation analysis around AdS${}_2$, which may correspond to the near-horizon geometry of the extremal BTZ black hole obtained from the TMG${}_{\Lambda }$ with identification upon uplifting three dimensions. A massive propagating scalar mode $\delta F$ satisfies the second-order differential equation away from the critical point of $K=l$, whose solution is given by the Bessel functions. On the other hand, $\delta F$ satisfies the fourth-order equation at the critical point. We exactly solve the fourth-order equation, and compare it with the log-gravity in two dimensions. Consequently, the critical gravity in two dimensions could not be described by a massless scalar $\delta F_{\mathrm{ml}}$ and its logarithmic partner $\delta F_{\log }^{4th}$.

17 pages, 3 figures

References in corpus (13)

• Massive Gravity in Three Dimensions
• Critical Gravity in Four Dimensions
• Critical Points of D-Dimensional Extended Gravities
• BTZ Black Hole with Chern-Simons and Higher Derivative Terms
• D-Dimensional Log Gravity
• Modes of Log Gravity
• A Simple Proof of the Chiral Gravity Conjecture
• Ghosts of Critical Gravity
• Canonical analysis of cosmological topologically massive gravity at the chiral point
• Classical stability of BTZ black hole in new massive gravity
• On Black Hole Stability in Critical Gravities
• Logarithmic conformal field theory approach to topologically massive gravity
• Topologically massive gravity on AdS${}_2$ spacetimes

Cited by in corpus (3)

• Holographic Renormalization and Stress Tensors in New Massive Gravity
• Linearized Modes in Extended and Critical Gravities
• Causality Constraint on Noncritical Einstein-Weyl Gravity