Scale-invariance at the core of quantum black holes

ORCID
0000-0001-7125-4372
Affiliation
Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada
Borissova, Johanna N;
GND
1144990971
ORCID
0000-0003-2701-9361
Affiliation
Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena
Held, Aaron;
Affiliation
Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada
Afshordi, Niayesh

We study spherically-symmetric solutions to a modified Einstein–Hilbert action with renormalization group (RG) scale-dependent couplings, inspired by Weinberg’s Asymptotic Safety scenario for quantum gravity. The RG 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 α = √ 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.

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