Black holes in effective loop quantum gravity: Covariant holonomy modifications

TL;DR

This paper derives covariant, scale-dependent holonomy-modified black hole solutions in loop quantum gravity, revealing a non-singular wormhole structure and new physical insights into holonomy parameters and thermodynamics.

Contribution

It provides the first covariant, exact vacuum black hole solutions with scale-dependent holonomy modifications in loop quantum gravity, demonstrating robustness and revealing new physical effects.

Findings

Reconstructed a non-singular wormhole space-time from different gauges.

Identified the distinction between constant and scale-dependent holonomy parameters.

Explored novel thermodynamical properties of the modified black holes.

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 non-singular 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 non-trivial 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.