# Dynamical renormalization of black-hole spacetimes

## TL;DR

This paper develops a self-consistent model of black-hole spacetimes incorporating the running of the gravitational coupling, leading to a non-singular, renormalized black hole solution if a fixed point exists in the RG flow.

## Contribution

It introduces a method to iteratively include quantum gravitational effects into black-hole spacetimes, resulting in a singularity-free, renormalized solution.

## Key findings

- Sequence converges to a non-singular, renormalized black-hole spacetime.
- The solution is analytically derived and depends on the RG flow fixed point.
- Potential implications for quantum gravity and black hole singularity resolution.

## Abstract

We construct a black-hole spacetime which includes the running of the gravitational coupling in a self-consistent way. Starting from a classical Schwarzschild black hole, the backreaction effects produced by the running Newton's coupling are taken into account iteratively. The sequence, described by a simple recurrence relation, flows towards a self-consistent solution that can be derived analytically. As a key result, if the gravitational renormalization group flow attains a non-trivial fixed point at high energies, the sequence converges to a "renormalized" black-hole spacetime of the Dymnikova-type, which is free of singularities.