[Paper Review] Black holes in asymptotically safe gravity and beyond

Astrid Eichhorn, Aaron Held|arXiv (Cornell University)|Dec 19, 2022

Noncommutative and Quantum Gravity Theories4 citations

TL;DR

This paper investigates black holes in asymptotically safe quantum gravity using Renormalization Group (RG) improvement to construct spacetimes that resolve classical curvature singularities and feature inner horizons even at zero spin. Key results include geodesic completeness, compact photon spheres, and cold remnants after Hawking evaporation, with observational constraints possible via electromagnetic and future gravitational-wave signatures, especially at near-critical spin.

ABSTRACT

Asymptotically safe quantum gravity is an approach to quantum gravity that achieves formulates a standard quantum field theory for the metric. Therefore, even the deep quantum gravity regime, that is expected to determine the true structure of the core of black holes, is described by a spacetime metric. The essence of asymptotic safety lies in a new symmetry of the theory -- quantum scale symmetry -- which characterizes the short-distance regime of quantum gravity. It implies the absence of physical scales. Therefore, the Newton coupling, which corresponds to a scale, namely the Planck length, must vanish asymptotically in the short-distance regime. This implies a weakening of the gravitational interaction, from which a resolution of classical spacetime singularities can be expected. In practise, properties of black holes in asymptotically safe quantum gravity cannot yet be derived from first principles, but are constructed using a heuristic procedure known as Renormalization Group improvement. The resulting asymptotic-safety inspired black holes have been constructed both for vanishing and for nonvanishing spin parameter. They are characterized by (i) the absence of curvature singularities, (ii) a more compact event horizon and photon sphere, (iii) a second (inner) horizon even at vanishing spin and (iv) a cold remnant as a possible final product of the Hawking evaporation. Observations can start to constrain the quantum-gravity scale that can be treated as a free parameter in asymptotic-safety inspired black holes. For slowly-spinning black holes, constraints from the EHT and X-ray observations can only constrain quantum-gravity scales far above the Planck length. In the limit of near-critical spin, asymptotic-safety inspired black holes may ``light up" in a way the ngEHT may be sensitive to, even for a quantum-gravity scale equalling the Planck length.

Motivation & Objective

• To investigate the structure and properties of black holes in asymptotically safe quantum gravity, where quantum scale symmetry prevents physical scales at short distances.
• To address the unresolved problem of spacetime singularities and Cauchy horizons in classical black holes by constructing quantum-gravity-corrected spacetimes.
• To develop a phenomenological framework—RG-improved black holes—that respects fundamental principles like regularity, locality, and simplicity, enabling observational tests.
• To assess the potential for current and future observations (e.g., Event Horizon Telescope, X-ray spectroscopy, gravitational waves) to constrain the quantum-gravity scale.
• To explore the viability of these models as proxies for full quantum gravity solutions, given the lack of dynamical equations from asymptotically safe gravity.

Proposed method

• Uses Renormalization Group (RG) improvement to construct black hole spacetimes by promoting gravitational couplings to scale-dependent functions, based on the running of couplings in asymptotically safe gravity.
• Applies the decoupling mechanism to ensure that quantum corrections vanish in the infrared, preserving standard GR behavior at large distances.
• Implements scale identification via the local curvature invariants to determine the RG scale for gravitational solutions, ensuring physical consistency.
• Constructs spherically symmetric and spinning (Kerr-type) black hole solutions by replacing the Newton constant with its scale-dependent version, leading to modified metric components.
• Analyzes spacetime structure, thermodynamics, and horizon properties (including inner horizons) in these RG-improved models.
• Evaluates observational constraints using electromagnetic data (EHT, X-ray reflection) and explores the potential for gravitational-wave ringdown signatures under strong theoretical assumptions.

Experimental results

Research questions

• RQ1 How do quantum corrections from asymptotically safe gravity resolve the classical curvature singularity in black holes?
• RQ2 What is the structure of the spacetime, including horizons and photon spheres, in RG-improved black holes with and without spin?
• RQ3 Can astrophysical observations constrain the quantum-gravity scale in these models, especially when it is not fixed to the Planck scale?
• RQ4 Under what conditions can near-critical spin black holes produce observable electromagnetic imprints detectable by the next-generation Event Horizon Telescope?
• RQ5 To what extent can gravitational-wave ringdown observations test these quantum-corrected black hole models, given the lack of a full dynamical equation?

Key findings

• Asymptotic-safety inspired black holes exhibit no curvature singularities and are geodesically complete, resolving a key issue in classical general relativity.
• The event horizon and photon sphere are more compact than in standard Schwarzschild or Kerr black holes, even at zero spin.
• A second (inner) horizon appears in the non-rotating case, indicating a richer causal structure than in classical black holes.
• Hawking evaporation may lead to a cold remnant as a final state, suggesting a potential endpoint of black hole evolution in this framework.
• For slowly spinning black holes, current electromagnetic observations (EHT and X-ray) constrain the quantum-gravity scale to values far above the Planck length.
• At near-critical spin, quantum-gravity effects may produce observable imprints detectable by the next-generation Event Horizon Telescope, even if the scale is at the Planck length.