Entropy-Product Rules for Charged Rotating Black Holes

TL;DR

This paper investigates the universal properties of entropy products in charged rotating black holes, revealing their dependence on quantized charges and angular momentum, with implications for higher-derivative gravities and gauge theories.

Contribution

It introduces a generalized framework for understanding entropy products in various gravity theories, highlighting their quantization and dependence on charges and angular momentum.

Findings

Entropy product depends on charges and angular momentum in Einstein gravity.

In higher-derivative gravity, entropy product depends only on angular momentum.

Quantization of entropy product persists in complex gravity theories.

Abstract

We study the universal nature of the product of the entropies of all horizons of charged rotating black holes. We argue, by examining further explicit examples, that when the maximum number of rotations and/or charges are turned on, the entropy product is expressed in terms of angular momentum and/or charges only, which are quantized. (In the case of gauged supergravities, the entropy product depends on the gauge-coupling constant also.) In two-derivative gravities, the notion of the "maximum number" of charges can be defined as being sufficiently many non-zero charges that the Reissner-Nordstrom black hole arises under an appropriate specialisation of the charges. (The definition can be relaxed somewhat in charged AdS black holes in $D\ge 6$.) In higher-derivative gravity, we use the charged rotating black hole in Weyl-Maxwell gravity as an example for which the entropy product is still quantized, but it is expressed in terms of the angular momentum only, with no dependence on the charge. This suggests that the notion of maximum charges in higher-derivative gravities requires further understanding.