# Scale-dependent planar Anti-de Sitter black hole

## TL;DR

This paper explores a new class of four-dimensional planar Anti-de Sitter black holes where fundamental couplings vary with the spatial coordinate, affecting their geometry and thermodynamics, thus extending classical solutions.

## Contribution

It introduces scale-dependent couplings into AdS black hole solutions, providing a novel family of solutions with variable parameters and analyzing their thermodynamic properties.

## Key findings

- Couplings become functions of the spatial coordinate z.
- Solutions differ from classical black holes in geometry and thermodynamics.
- Thermodynamic analysis reveals modified properties due to scale dependence.

## Abstract

In this work, we investigate four-dimensional planar black hole solutions in anti-de Sitter spacetimes in light of the so-called scale-dependent scenario. To obtain this new family of solutions, the classical couplings of the theory, i.e., the gravitational coupling and the cosmological constant, are not taken to be fixed values anymore. Thus, those classical parameters evolve to functions which change along the "height" coordinate, z. The effective Einstein field equations are solved, and the results are analyzed and compared with the classical counterpart. Finally, some thermodynamic properties of the presented scale--dependent black hole are investigated.