# BTZ black hole assuming running couplings

## TL;DR

This paper explores a generalized BTZ black hole model incorporating scale-dependent couplings, deriving solutions from an effective action, analyzing thermodynamics, and proposing an alternative method for Newton coupling determination.

## Contribution

It introduces a novel approach to include scale-dependent couplings in BTZ black holes using effective action and null energy conditions.

## Key findings

- Derived self-consistent solutions for the lapse function and couplings.
- Analyzed the asymptotic behavior and thermodynamics of the generalized black hole.
- Presented an alternative method for obtaining the scale-dependent Newton coupling.

## Abstract

In the present work a generalization of the BTZ black hole is studied, for the case of scale dependent couplings. One starts by using the effective action for scale dependence couplings to get a generalization of the Einstein field equations. Self consistent solutions for lapse function, cosmological coupling and Newtons coupling are found. The effect of scale dependent couplings with respect to the classical solution is shown. Moreover, asymptotic behavior as well as thermodynamic properties were investigated. Finally, an alternative way to get the scale dependent Newton coupling, from the so-called "Null Energy Condition" is presented.