# Five-dimensional scale-dependent black holes with constant curvature and Solv horizons

## TL;DR

This paper introduces five-dimensional scale-dependent black hole solutions with various horizon geometries, including constant curvature and Solv types, by allowing gravitational and cosmological couplings to vary with radius, affecting their thermodynamic properties.

## Contribution

It presents novel five-dimensional scale-dependent black hole solutions with Thurston geometries, extending classical solutions by incorporating radius-dependent couplings inspired by high energy physics.

## Key findings

- New scale-dependent black hole solutions with Thurston geometries.
- The topology and running parameter influence asymptotic structure.
- Differences in entropy and temperature compared to classical solutions.

## Abstract

In this work, we investigate five-dimensional scale-dependent black hole solutions by modelling their event horizon with some of the eight Thurston three-dimensional geometries. Specifically, we construct constant curvature scale-dependent black holes and also the more exotic scale-dependent Solv black hole. These new solutions are obtained by promoting both the gravitational and the cosmological couplings to $r$-dependent functions, in light of a particular description of the effective action inspired by the high energy philosophy. Interestingly, the so-called running parameter, together with the topology of the event horizon, control the asymptotic structure of the solutions found. Finally, differences in both the entropy and the temperature between the classical and the scale-dependent Solv black hole are briefly commented.