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

TL;DR

This paper explores exact solutions in topologically massive gravity coupled with electrodynamics at special coupling values, revealing new black hole solutions and their holographic properties, especially at the chiral point where the extremal BTZ black hole becomes massless.

Contribution

It presents new exact solutions at special coupling constants, including a massless extremal BTZ black hole at the chiral point and electrically charged solutions with different asymptotic behaviors.

Findings

Massless extremal BTZ black hole at the chiral point.

Existence of electrically charged solutions with asymptotic AdS_3.

Solutions obey weakened asymptotic boundary conditions.

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 l\mu_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 Ba\~nados-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 l\mu_G=1+2l\mu_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.