[Paper Review] Regular black holes from Loop Quantum Gravity

Abhay Ashtekar, Javier Olmedo+1 more|arXiv (Cornell University)|Jan 3, 2023

Noncommutative and Quantum Gravity Theories4 citations

TL;DR

This paper proposes that loop quantum gravity (LQG) resolves black hole singularities via quantum geometry effects, replacing the classical singularity with a quantum bounce. Using effective dynamics in symmetric models, it shows curvature invariants remain bounded, horizons evolve unitarily, and information loss is avoided—offering a consistent, non-singular spacetime structure for black holes from formation to evaporation.

ABSTRACT

There is rich literature on regular black holes from loop quantum gravity (LQG), where quantum geometry effects resolve the singularity, leading to a quantum extension of the classical space-time. As we will see, the mechanism that resolves the singularity can also trigger conceptually undesirable features that can be subtle and are often uncovered only after a detailed examination. Therefore, the quantization scheme has to be chosen rather astutely. We illustrate the new physics that emerges first in the context of the eternal black hole represented by the Kruskal space-time in classical general relativity, then in dynamical situations involving gravitational collapse, and finally, during the Hawking evaporation process. The emphasis is on novel conceptual features associated with the causal structure, trapping and anti-trapping horizons and boundedness of invariants associated with curvature and matter. This Chapter is not intended to be an exhaustive account of all LQG results on non-singular black holes. Rather, we have selected a few main-stream thrusts to anchor the discussion, and provided references where further details as well as discussions of related developments can be found. In the spirit of this Volume, the goal is to present a bird's eye view that is accessible to a broad audience.

Motivation & Objective

• To investigate whether loop quantum gravity (LQG) resolves the spacetime singularity in black holes, as it does in cosmological models.
• To analyze the causal structure, trapping/anti-trapping horizons, and curvature invariants in quantum-corrected black hole spacetimes.
• To address the black hole information paradox by showing unitary evolution and entropy conservation in LQG-based models.
• To contrast LQG results with other approaches such as the firewall scenario and AdS/CFT-based no-transmission principles.
• To highlight conceptual differences between young and old black holes in LQG, especially regarding quantum entanglement and horizon degrees of freedom.

Proposed method

• Adopting effective dynamics from loop quantum gravity to model quantum corrections in symmetric spacetimes, particularly the Kruskal and Kantowski-Sachs geometries.
• Using symmetry-reduced models and effective equations to describe the quantum bounce at the singularity, replacing the classical curvature blow-up.
• Applying Euclidean quantum field theory techniques to compute corrections to Hawking temperature and quasi-normal mode frequencies.
• Constructing global spacetime diagrams that extend the classical Kruskal solution into the quantum regime, preserving causal structure and horizon dynamics.
• Analyzing the behavior of trapped and anti-trapped regions during gravitational collapse and evaporation, focusing on the role of quantum geometry in stabilizing curvature invariants.
• Comparing results with classical general relativity and other quantum gravity approaches to assess consistency with semi-classical expectations and unitarity.

Experimental results

Research questions

• RQ1 Can quantum geometry effects in LQG resolve the spacelike singularity in the Schwarzschild black hole, as they do in loop quantum cosmology?
• RQ2 How does the causal structure—particularly the behavior of trapping and anti-trapping horizons—change in the quantum regime?
• RQ3 Do curvature invariants such as the Kretschmann scalar remain bounded in the quantum extension, indicating a non-singular spacetime?
• RQ4 Is information preserved during black hole evaporation in the LQG framework, and how does this compare to the firewall or no-communication scenarios?
• RQ5 What distinguishes the internal and external structure of a young black hole from an old one in LQG, especially regarding quantum entanglement and horizon entropy?

Key findings

• Quantum geometry effects in LQG lead to a quantum bounce at the black hole singularity, replacing the classical curvature blow-up with a non-singular, bounded spacetime extension.
• Curvature invariants such as the Kretschmann scalar remain bounded in the quantum regime, indicating a resolution of the classical singularity without pathologies.
• The causal structure is preserved in the quantum extension, with well-defined trapping and anti-trapping horizons that evolve unitarily through collapse and evaporation.
• Hawking evaporation in LQG is consistent with unitarity: the number of outgoing and ingoing quanta remains entangled, and information is not lost.
• Old black holes—those that have evaporated for $\sim 10^{64}$ years—exhibit vastly different internal and external quantum structures compared to young black holes of the same mass, despite identical horizon areas.
• The area of the dynamical horizon remains a measure of surface degrees of freedom in LQG, even for old black holes, but these degrees of freedom are entangled with a large number of quanta in the exterior and trapped regions.