Towards the emergence of non-zero thermodynamical quantities for Lanczos-Lovelock black holes dressed with a scalar field

TL;DR

This paper investigates Lanczos-Lovelock black holes with scalar fields and non-linear Maxwell fields, revealing non-zero thermodynamical quantities and analyzing their stability, satisfying fundamental thermodynamic laws.

Contribution

It introduces a model with scalar and non-linear Maxwell fields in Lanczos-Lovelock gravity that yields non-zero thermodynamic quantities, unlike previous versions.

Findings

Non-zero thermodynamical quantities for the black holes.

Solutions satisfy the First Law of Thermodynamics.

Thermodynamical stability analysis conducted.

Abstract

The present work aims to explore the model given by Lanczos-Lovelock gravity theories indexed by a fixed integer to require a unique anti-de Sitter vacuum, dressed by a scalar field non-minimal coupling. For this model, we add a special matter source characterized by a non-linear Maxwell field coupling with a function depending on the scalar field. Computing its thermodynamics parameters by using the Euclidean action, we obtain interesting and non zero thermodynamical quantities, unlike its original version, allowing analyzing thermodynamical stability. Together with the above, we found that these solutions satisfy the First Law of Thermodynamics as well as a Smarr relation.