Charged BTZ-like black holes in higher dimensions

Abstract

Motivated by many worthwhile paper about (2 + 1)-dimensional BTZ black holes, we generalize them to to (n + 1)-dimensional solutions, so called BTZ-like solutions. We show that the electric field of BTZ-like solutions is the same as (2 + 1)-dimensional BTZ black holes, and also their lapse functions are approximately the same, too. By these similarities, it is also interesting to investigate the geometric and thermodynamics properties of the BTZ-like solutions. We find that, depending on the metric parameters, the BTZ-like solutions may be interpreted as black hole solutions with inner (Cauchy) and outer (event) horizons, an extreme black hole or naked singularity. Then, we calculate thermodynamics quantities and conserved quantities, and show that they satisfy the first law of thermodynamics. Finally, we perform a stability analysis in the canonical ensemble and show that the BTZ-like solutions are stable in the whole phase space.