On the R\'enyi entropy of Lifshitz and hyperscaling violating black holes

TL;DR

This paper investigates Rényi entropies in Lifshitz and hyperscaling violating geometries, analyzing their properties, dual spectra, and stability constraints for specific parameters and limits.

Contribution

It provides new calculations of Rényi entropies for these geometries, explores the ground state spectrum, and derives stability constraints from entropy inequalities.

Findings

Ground state is unique in certain parameter ranges in the large $d- heta$ limit.

Rényi entropies are computed perturbatively around $n=1$.

Stability constraints are derived from entropy inequalities.

Abstract

We study R\'enyi entropies for geometries with Lifshitz scaling and hyperscaling violation. We calculate them for specific values of the Lifshitz parameter, and analyze the dual spectrum of the ground state. In the large $d-\theta$ limit they show that the ground state is unique in specific parameter ranges. We also calculate the R\'enyi entropies perturbatively around $n=1$, and derive constraints using the R\'enyi entropy inequalities, which correspond to the thermodynamic stability of the black holes.