Entropy product of rotating black holes in three-dimensions

TL;DR

This paper examines whether the universal entropy product rule for black holes applies in three-dimensional gravity models, finding it holds in some cases but not when certain anomalous terms are present.

Contribution

It investigates the universality of the entropy product in three-dimensional rotating black holes within different gravity theories, highlighting the impact of gravitational anomalies.

Findings

Entropy product is universal in new massive gravity.

Universality breaks down in minimal massive gravity with anomalies.

Thermodynamic properties of these black holes are also analyzed.

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.