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

TL;DR

The paper constructs exact solutions to CTMG coupled to TME at special couplings, revealing a massless ground state at the chiral point and a one-parameter vacuum family connected to extremal BTZ; it then generalizes to electrically charged solutions, which form a logarithmic self-dual branch and remain asymptotically AdS$_3$ under strengthened boundary conditions. The analysis leverages holographic boundary stress-tensor methods to compute conserved charges and uses a CM-inspired reduction to relate these geometries to self-dual (logarithmic) sectors. An Addendum shows the uncharged logarithmic solution persists in generalized massive gravity including NMG, extending the relevance of these Log Gravity-like backgrounds and their boundary structure.

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.