# Microscopic entropy of higher-dimensional nonminimally dressed Lifshitz black holes

## TL;DR

This paper computes the microscopic entropy of higher-dimensional Lifshitz black holes with scalar fields using a generalized Cardy-like formula, confirming its consistency with gravitational entropy and thermodynamics.

## Contribution

It introduces a higher-dimensional anisotropic Cardy-like formula for Lifshitz black holes with scalar fields, extending previous methods to arbitrary dimensions.

## Key findings

- Microscopic entropy matches Wald entropy for all configurations.
- Global charges satisfy the first law of thermodynamics.
- Configurations obey an anisotropic higher-dimensional Smarr formula.

## Abstract

In arbitrary dimension, we consider a theory described by the most general quadratic curvature corrections of Einstein gravity together with a self-interacting nonminimally coupled scalar field. This theory is shown to admit five different families of Lifshitz black holes dressed with a nontrivial scalar field. The entropy of these configurations is microscopically computed by means of a higher-dimensional anisotropic Cardy-like formula where the role of the ground state is played by the soliton obtained through a double analytic continuation. This involves to calculate the correct expressions for the masses of the higher-dimensional Lifshitz black hole as well as their corresponding soliton. The robustness of this Cardy-like formula is checked by showing that the microscopic entropy is in perfect agreement with the gravitational Wald entropy. Consequently, the calculated global charges are compatible with the first law of thermodynamics. We also verify that all the configurations satisfy an anisotropic higher-dimensional version of the Smarr formula.