Semi-classical central charge in topologically massive gravity

Abstract

It is shown that the warped black holes geometries discussed recently in 0807.3040 admit an algebra of asymptotic symmetries isomorphic to the semi-direct product of a Virasoro algebra and an algebra of currents. The realization of this asymptotic symmetry by canonical charges allows one to find the central charge of the Virasoro algebra. The right-moving central charge $c_R=\frac{(5{\hat{\nu }}^2+3)l}{G\hat{\nu }({\hat{\nu }}^2+3)}$ is obtained when the Virasoro generators are normalized in order to have a positive zero mode spectrum for the warped black holes. The current algebra is also shown to be centrally-extended.

major sign mistake in the central charge corrected. Conclusion adapted. Minor typos corrected

References in corpus (4)

• Surface charge algebra in gauge theories and thermodynamic integrability
• Black hole mass and angular momentum in topologically massive gravity
• Black Hole Entropy in the presence of Chern-Simons Terms
• Three-dimensional Chern-Simons black holes

Cited by in corpus (8)

• Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity
• Note on New Massive Gravity in $Ad{S}_3$
• On the Generalized Massive Gravity in $Ad{S}_3$
• Asymptotically AdS_3 Solutions to Topologically Massive Gravity at Special Values of the Coupling Constants
• Hawking radiation from covariant anomalies in 2+1 dimensional black holes
• Warped AdS_5 Black Holes and Dual CFTs
• Topologically massive gravity on AdS${}_2$ spacetimes
• Entropy of extremal warped black holes