Black holes and running couplings: A comparison of two complementary approaches

TL;DR

This paper compares two approaches to incorporating quantum effects into black hole solutions, highlighting their surprising agreement despite different methodologies within the context of quantum gravity.

Contribution

It presents a comparative analysis of the renormalization group improvement and exact solution methods for quantum black holes, emphasizing their conceptual and quantitative similarities.

Findings

Both approaches yield similar 'quantum' black hole pictures.

The methods incorporate scale-dependent gravitational couplings.

Results support the robustness of quantum black hole models.

Abstract

Black holes appear as vacuum solutions of classical general relativity which depend on Newton's constant and possibly the cosmological constant. At the level of a quantum field theory, these coupling constants typically acquire a scale-dependence. This proceedings briefly summarizes two complementary ways to incorporate this effect: the renormalization group improvement of the classical black hole solution based on the running couplings obtained within the gravitational Asymptotic Safety program and the exact solution of the improved equations of motion including an arbitrary scale dependence of the gravitational couplings. Remarkably the picture of the "quantum" black holes obtained from these very different improvement strategies is surprisingly similar.