Asymptotically AdS_3 Solutions to Topologically Massive Gravity at Special Values of the Coupling Constants

Abstract

We study exact solutions to Cosmological Topologically Massive Gravity (CTMG) coupled to Topologically Massive Electrodynamics (TME) at special values of the coupling constants. For the particular case of the so called chiral point lμ_G=1, vacuum solutions (with vanishing gauge field) are exhibited. These correspond to a one-parameter deformation of GR solutions, and are continuously connected to the extremal Bañados-Teitelboim-Zanelli black hole (BTZ) with bare constants J=-lM. At the chiral point this extremal BTZ turns out to be massless, and thus it can be regarded as a kind of ground state. Although the solution is not asymptotically AdS_3 in the sense of Brown-Henneaux boundary conditions, it does obey the weakened asymptotic recently proposed by Grumiller and Johansson. Consequently, we discuss the holographic computation of the conserved charges in terms of the stress-tensor in the boundary. For the case where the coupling constants satisfy the relation lμ_G=1+2lμ_E, electrically charged analogues to these solutions exist. These solutions are asymptotically AdS_3 in the strongest sense, and correspond to a logarithmic branch of selfdual solutions previously discussed in the literature.

16 pages; v2: references added, changes in the discussion of causal structure, comments on the relation with pp-wave solutions were included. Version v4 includes some comments on NMG

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• Asymptotically anti-de Sitter spacetimes in topologically massive gravity
• On the Generalized Massive Gravity in $Ad{S}_3$
• Hawking radiation from covariant anomalies in 2+1 dimensional black holes
• Witten-Nester Energy in Topologically Massive Gravity