Entropy product of rotating black holes in three-dimensions

Abstract

It has been shown that the product of the entropies of the inner Cauchy and outer event horizon of the charged axisymmetric and stationary black holes is a universal formula, which is independent of the black hole's mass. In this paper, we investigate this universality for the two kinds of rotating black holes in the three-dimensional gravity models. In fact, we study the spacelike warped anti-de Sitter black hole in the new massive gravity and the Ba~nados, Teitelboim, and Zanelli black hole in the minimal massive gravity. We show that this rule is held in the first theory. By contrast, in the latter case which includes a holographic gravitational anomalous term, we obtain that the universality does not work and the product depends on the mass. As a complement to the above verification, we also study the thermodynamic properties of these black holes.