Three-dimensional black holes with quintessence

Abstract

We study a quintessential black hole solution in three dimensions, with mass and quintessence charge. By exploring the Carter-Penrose diagram, we show the presence of spacelike and lightlike singularities in the metric, given different values for the quintessence parameter, as well as an AdS-like spatial infinity and event horizon encapsulating the singularity. We also study the propagation of scalar and Dirac (Weyl) fields around the black hole solutions with different quintessence charges obtaining the quasinormal spectra for both fields using two different numerical methods with good agreement between the data. In both cases, the presence of quintessence increases the imaginary part of the quasinormal mode, since this is related to the event horizon of the solution, preserving the interpretation of this quantity as relaxation time in the corresponding CFT. We also investigate the behavior of high-temperature scalar field modes, demonstrating the presence of the so-called hydrodynamical limit, differently from the BTZ black hole, for which no such modes exist.