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Black holes in effective loop quantum gravity: Covariant holonomy modifications

Idrus Husin Belfaqih1,*, Martin Bojowald2,†, Suddhasattwa Brahma1,‡, and Erick I. Duque1,§

  • 1Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, Scotland, United Kingdom
  • 2Institute for Gravitation and the Cosmos, The Pennsylvania State University, 104 Davey Laboratory, University Park, Pennsylvania 16802, USA

  • *Contact author: i.h.belfaqih@sms.ed.ac.uk
  • †Contact author: bojowald@psu.edu
  • ‡Contact author: suddhasattwa.brahma@gmail.com
  • §Contact author: eqd5272@psu.edu
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Phys. Rev. D 112, 046022 – Published 27 August, 2025

DOI: https://doi.org/10.1103/1tyh-87sr

Abstract

Emergent modified gravity provides a covariant, effective framework for obtaining spherically symmetric black hole solutions in models of loop quantum gravity with scale-dependent holonomy modifications. Exact solutions for vacuum black holes in the presence of a cosmological constant are derived here and analyzed in four different gauges, explicitly related to one another by standard coordinate transformations. The global structure is obtained by gluing space-time regions corresponding to the gauge choices, reconstructing a nonsingular wormhole space-time for an arbitrary scale-dependent holonomy parameter. This outcome demonstrates the robustness of black-hole models with covariant holonomy modifications under quantization ambiguities. Compared with previous constructions, full covariance of the resulting space-time models as derived here implies subtle new effects and leads to a novel understanding of the parameters in holonomy modifications, distinguishing a constant holonomy length from a possibly scale-dependent function that may change coefficients of holonomy terms. New physical results are obtained for instance in the context of a nontrivial zero-mass limit of holonomy-modified space-times. The existence of a consistent effective space-time structure implies various novel aspects of a net gravitational stress-energy and related thermodynamical properties.

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Phys. Rev. D 112, 046022– Published 27 August, 2025
  • Received 23 September 2024
  • Accepted 1 August 2025
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