Studies of transport coefficients in charged AdS$_{4}$ black holes on $\kappa$-deformed space

TL;DR

This paper investigates how $3$-deformed space influences thermodynamic properties and electrical conductivity of charged AdS$_{4}$ black holes using holographic renormalization within an Einstein-Maxwell framework.

Contribution

It introduces a novel $3$-deformed space approach to analyze thermodynamics and transport in charged AdS$_{4}$ black holes, extending previous models with Kaniadakis-inspired deformation.

Findings

Deformation affects thermodynamic quantities derived from holographic renormalization.

Electrical conductivity is computed in the deformed space scenario.

The model provides insights into the impact of $3$-deformation on black hole physics.

Abstract

In this work, we study the effect of $\kappa$-deformed space on the thermodynamic quantities, this are find through the holographic renormalization that provide the free energy, which is fundamental to derive the another thermodynamic quantities. For this scenario we consider an charged AdS$_{4}$ black hole for an Einstein-Maxwell model where the derivative quadrivector is replaced by a deformed version inspired in Kaniadakis statistics. Besides, we extract the transport coefficient know as electrical conductivity.