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Black Holes in Asymptotic Safety: A Review of Solutions and Phenomenology

Andrea Spina

TL;DR

The review analyzes black holes in the Asymptotic Safety framework, focusing on RG-improved and effective-action constructions that replace central singularities with regular cores while preserving Schwarzschild asymptotics. It covers static solutions (Bonanno–Reuter, Hayward, Dymnikova) and dynamical collapse models that implement running gravitational couplings during formation, exploring quasinormal modes, Hawking temperature, and shadows. A common outcome is the suppression of Hawking temperature near extremality and a modest overall deviation in observables, with stronger signatures appearing in higher overtones, near-extremal thermodynamics, or evaporation dynamics. The work connects quantum gravity predictions to astrophysical observables such as gravitational waves and black-hole shadows, while noting open issues in RG scale identification and truncation dependence that merit further study.

Abstract

Asymptotic Safety offers a conservative and predictive framework for quantum gravity, based on the existence of a renormalization group fixed point that ensures ultraviolet completeness without introducing new degrees of freedom. Black holes provide a natural arena in which to explore the implications of this scenario, as they probe the strongest gravitational fields and highlight the shortcomings of classical general relativity. In recent years, a variety of quantum-corrected black-hole solutions have been constructed within the Asymptotic Safety approach, either by renormalization-group improvement of classical metrics or through effective actions inspired by the flow of couplings. This review summarizes the current status of these developments. We discuss the structure and properties of the proposed solutions, their thermodynamics and evaporation, and their dynamical aspects such as quasinormal modes and shadows.

Black Holes in Asymptotic Safety: A Review of Solutions and Phenomenology

TL;DR

The review analyzes black holes in the Asymptotic Safety framework, focusing on RG-improved and effective-action constructions that replace central singularities with regular cores while preserving Schwarzschild asymptotics. It covers static solutions (Bonanno–Reuter, Hayward, Dymnikova) and dynamical collapse models that implement running gravitational couplings during formation, exploring quasinormal modes, Hawking temperature, and shadows. A common outcome is the suppression of Hawking temperature near extremality and a modest overall deviation in observables, with stronger signatures appearing in higher overtones, near-extremal thermodynamics, or evaporation dynamics. The work connects quantum gravity predictions to astrophysical observables such as gravitational waves and black-hole shadows, while noting open issues in RG scale identification and truncation dependence that merit further study.

Abstract

Asymptotic Safety offers a conservative and predictive framework for quantum gravity, based on the existence of a renormalization group fixed point that ensures ultraviolet completeness without introducing new degrees of freedom. Black holes provide a natural arena in which to explore the implications of this scenario, as they probe the strongest gravitational fields and highlight the shortcomings of classical general relativity. In recent years, a variety of quantum-corrected black-hole solutions have been constructed within the Asymptotic Safety approach, either by renormalization-group improvement of classical metrics or through effective actions inspired by the flow of couplings. This review summarizes the current status of these developments. We discuss the structure and properties of the proposed solutions, their thermodynamics and evaporation, and their dynamical aspects such as quasinormal modes and shadows.
Paper Structure (14 sections, 46 equations, 1 figure, 3 tables)

This paper contains 14 sections, 46 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Asymptotic Safety Framework
  3. Static Black Holes from RG Improvement
  4. Bonanno-Reuter Metric
  5. Hayward Metric
  6. Dymnikova Metric
  7. Dynamical Black Holes from Gravitational Collapse
  8. Proper Time Approach
  9. Scheme B ($\varepsilon=1$)
  10. Scheme C ($\varepsilon=0$)
  11. Quasinormal Modes
  12. Hawking Temperature
  13. Shadows
  14. Conclusions

Figures (1)

  • Figure 1: Metric functions $f(R)$ for all the regular black hole solutions at their critical values with $M=3.503$ (critical mass for B-R).