Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity

TL;DR

This paper explores various exact solutions in three-dimensional BHT massive gravity, including black holes, solitons, kinks, and wormholes, revealing their properties, thermodynamics, and asymptotic behaviors across different cosmological constant regimes.

Contribution

It provides new explicit solutions such as black holes, solitons, and wormholes in BHT massive gravity, expanding understanding of their geometric and thermodynamic properties.

Findings

Black holes characterized by mass and gravitational hair parameters.

Existence of regular gravitational solitons and kinks from Wick rotations.

Wormhole solutions interpolating between negative curvature universes.

Abstract

The theory of massive gravity in three dimensions recently proposed by Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the theory admits a unique maximally symmetric solution, a conformally flat space that contains black holes and gravitational solitons for any value of the cosmological constant is found. For negative cosmological constant, the black hole is characterized in terms of the mass and the "gravitational hair" parameter, providing a lower bound for the mass. For negative mass parameter, the black hole acquires an inner horizon, and the entropy vanishes at the extremal case. Gravitational solitons and kinks, being regular everywhere, are obtained from a double Wick rotation of the black hole. A wormhole solution in vacuum that interpolates between two static universes of negative spatial curvature is obtained as a limiting case of the gravitational soliton with a suitable identification. The black hole and the gravitational soliton fit within a set of relaxed asymptotically AdS conditions as compared with the ones of Brown and Henneaux. In the case of positive cosmological constant the black hole possesses an event and a cosmological horizon, whose mass is bounded from above. Remarkably, the temperatures of the event and the cosmological horizons coincide, and at the extremal case one obtains the analogue of the Nariai solution, $dS_{2}\times S^{1}$. A gravitational soliton is also obtained through a double Wick rotation of the black hole. The Euclidean continuation of these solutions describes instantons with vanishing Euclidean action. For vanishing cosmological constant the black hole and the gravitational soliton are asymptotically locally flat spacetimes. The rotating solutions can be obtained by boosting the previous ones in the $t-\phi$ plane.