Exact black hole solution for scale dependent gravitational couplings and the corresponding coupling flow

TL;DR

This paper derives an exact black hole solution within a scale-dependent gravity framework, revealing how gravitational couplings evolve and comparing this flow to the renormalization group approach.

Contribution

It provides a novel exact black hole solution with scale-dependent couplings derived from the field equations, and analyzes the flow of these couplings.

Findings

Derived a non-trivial symmetrical black hole solution with scale-dependent G(r) and Lambda(r)

Established a classical-like choice of integration constants

Compared the coupling flow to the exact renormalization group flow

Abstract

We study a black hole solution for the generalized Einstein Hilbert action with scale dependent couplings G(r) and Lambda(r). The form of the couplings is not imposed, but rather deduced from the existence of a non trivial symmetrical solution. A classical-like choice of the integration constants is found. Finally, the induced flow of the couplings is derived and compared to the flow that is obtained in the context of the exact renormalization group approach.