# A Cardy-like formula for rotating black holes with planar horizon

## TL;DR

This paper derives a Cardy-like formula for calculating the entropy of various rotating planar black holes in higher dimensions, linking it to vacuum energy and gravitational solitons, and validates it across multiple black hole types.

## Contribution

It introduces a novel Cardy-like entropy formula that does not rely on central charges but uses vacuum energy from gravitational solitons, applicable to diverse black hole solutions.

## Key findings

- The formula accurately computes entropy for AdS, Lifshitz, and hyperscaling violation black holes.
- The vacuum energy is identified with a gravitational bulk soliton obtained via double analytic continuation.
- The approach is robust across various black hole geometries.

## Abstract

We show that the semiclassical entropy of $D$-dimensional rotating (an)isotropic black holes with planar horizon can be successfully computed according to a Cardy-like formula. This formula does not refer to any central charges but instead involves the vacuum energy which is identified with a gravitational bulk soliton. The soliton is obtained from the non-rotating black hole solution by means of a double analytic continuation. The robustness of the Cardy-like formula is tested with numerous and varied examples, including AdS, Lifshitz and hyperscaling violation planar black holes.