Scale-invariance at the core of quantum black holes

TL;DR

This paper explores quantum black holes using a modified gravity model with scale-dependent couplings, revealing a shift of the infinite temperature point to the origin and a scale-invariant interior structure.

Contribution

It introduces a novel approach linking the Renormalization Group scale to black hole thermodynamics, providing analytical and numerical solutions that interpolate between classical and quantum regimes.

Findings

The infinite temperature point shifts from the horizon to the origin.

Interior solutions exhibit scale-invariance characterized by a specific power law.

Deviations from classical black holes occur near the Planck scale, potentially observable.

Abstract

We study spherically-symmetric solutions to a modified Einstein-Hilbert action with Renormalization Group scale-dependent couplings, inspired by Weinberg's Asymptotic Safety scenario for Quantum Gravity. The Renormalization Group scale is identified with the Tolman temperature for an isolated gravitational system in thermal equilibrium with Hawking radiation. As a result, the point of infinite local temperature is shifted from the classical black-hole horizon to the origin and coincides with a timelike curvature singularity. Close to the origin, the spacetime is determined by the scale-dependence of the cosmological constant in the vicinity of the Reuter fixed point: the free components of the metric can be derived analytically and are characterized by a radial power law with exponent $\alpha = \sqrt{3}-1$. Away from the fixed point, solutions for different masses are studied numerically and smoothly interpolate between the Schwarzschild exterior and the scale-invariant interior. Whereas the exterior of objects with astrophysical mass is described well by vacuum General Relativity, deviations become significant at a Planck distance away from the classical horizon and could lead to observational signatures. We further highlight potential caveats in this intriguing result with regard to our choice of scale-identification and identify future avenues to better understand quantum black holes in relation to the key feature of scale-invariance.