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1. Black-Hole Models in Loop Quantum Gravity

   https://doi.org/10.3390/universe6080125  

   Bojowald, Martin (August 2020, Universe)

   null (Ed.)

   Dynamical black-hole scenarios have been developed in loop quantum gravity in various ways, combining results from mini and midisuperspace models. In the past, the underlying geometry of space-time has often been expressed in terms of line elements with metric components that differ from the classical solutions of general relativity, motivated by modified equations of motion and constraints. However, recent results have shown by explicit calculations that most of these constructions violate general covariance and slicing independence. The proposed line elements and black-hole models are therefore ruled out. The only known possibility to escape this sentence is to derive not only modified metric components but also a new space-time structure which is covariant in a generalized sense. Formally, such a derivation is made available by an analysis of the constraints of canonical gravity, which generate deformations of hypersurfaces in space-time, or generalized versions if the constraints are consistently modified. A generic consequence of consistent modifications in effective theories suggested by loop quantum gravity is signature change at high density. Signature change is an important ingredient in long-term models of black holes that aim to determine what might happen after a black hole has evaporated. Because this effect changes the causal structure of space-time, it has crucial implications for black-hole models that have been missed in several older constructions, for instance in models based on bouncing black-hole interiors. Such models are ruled out by signature change even if their underlying space-times are made consistent using generalized covariance. The causal nature of signature change brings in a new internal consistency condition, given by the requirement of deterministic behavior at low curvature. Even a causally disconnected interior transition, opening back up into the former exterior as some kind of astrophysical white hole, is then ruled out. New versions consistent with both generalized covariance and low-curvature determinism are introduced here, showing a remarkable similarity with models developed in other approaches, such as the final-state proposal or the no-transition principle obtained from the gauge-gravity correspondence. 

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2. Smooth extensions of black holes in loop quantum gravity

   https://doi.org/10.1142/S0218271823501018  

   Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge (December 2023, International Journal of Modern Physics D)

   Vacuum spherically symmetric loop quantum gravity in the midi-superspace approximation using inhomogeneous horizon-penetrating slices has been studied for a decade, and it has been noted that the singularity is eliminated. It is replaced by a region of high curvature and potentially large quantum fluctuations. It was recently pointed out that the effective semiclassical metric implies the existence of a shell of matter which violates energy conditions in regions where the curvature is largest. Here, we propose an alternative way of treating the problem that is free from the shells. The ambiguity in the treatment is related with the existence of new observables in the quantum theory that characterize the area excitations, and how the counterpart of diffeomorphisms in the discrete quantum theory is mapped to the continuum semiclassical picture. The resulting spacetime in the high curvature region inside the horizon is approximated by a metric of the type of the Simpson–Visser wormhole and it connects the black hole interior to a white hole in a smooth manner. 

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3. Properties of a recent quantum extension of the Kruskal Geometry

   https://doi.org/10.1142/S0218271820500765  

   Ashtekar, Abhay; Olmedo, Javier (July 2020, International Journal of Modern Physics D)

   Recently it was shown that, in an effective description motivated by loop quantum gravity, singularities of the Kruskal space-time are naturally resolved \cite{aoslett,aos}. In this note we explore a few properties of this quantum corrected effective metric. In particular, we (i) calculate the Hawking temperature associated with the horizon of the effective geometry and show that the quantum correction to the temperature is completely negligible for macroscopic black holes, just as one would hope; (ii) discuss the subtleties associated with the asymptotic properties of the space-time metric, and show that the metric is asymptotically flat in a precise sense; (iii) analyze the asymptotic fall-off of curvature; and, (iv) show that the ADM energy is well-defined (and agrees with that determined by the horizon area), even though the curvature falls off less rapidly than in the standard asymptotically flat context. 

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4. Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity

   https://doi.org/10.1007/s41114-023-00046-1  

   Mertens, Thomas G.; Turiaci, Gustavo J. (December 2023, Living Reviews in Relativity)

   Abstract We review recent developments in Jackiw–Teitelboim gravity. This is a simple solvable model of quantum gravity in two dimensions (that arises e.g. from the s-wave sector of higher dimensional gravity systems with spherical symmetry). Due to its solvability, it has proven to be a fruitful toy model to analyze important questions such as the relation between black holes and chaos, the role of wormholes in black hole physics and holography, and the way in which information that falls into a black hole can be recovered. 

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5. Spacetime surgery for black hole fireworks

   https://doi.org/10.1088/1475-7516/2025/01/098  

   Lin, Wei-Chen; Yeom, Dong-han; Stojkovic, Dejan (January 2025, Journal of Cosmology and Astroparticle Physics)

   Abstract We construct an explicit model for the black hole to white hole transition (known as the black hole fireworks scenario) using the cut-and-paste technique. We model a black hole collapse using the evolution of a time-like shell in the background of the loop quantum gravity inspired metric and then the space-like shell analysis to construct the firework geometry. Our simple and well-defined analysis removes some subtle issues that were present in the previous literature [1] and makes the examination of the junction conditions easier. We further point out that the infalling and asymptotic observers, both in ours and the original scenario in ref. [1], encounter quite different physics. While the proper time of the bounce for an infalling observer can be determined without ambiguity, the bouncing time interval for the asymptotic observer can be chosen arbitrarily by changing how one cuts and pastes the spacetimes outside the event horizons. It is puzzling that the proper time of a distant (rather than infalling) observer is subject to randomness since the infalling observer is supposed to experience a stronger quantum gravity effect. This result might suggest that a black hole firework scenario does not allow for the existence of an effectively classical spacetime inside the horizon. The main message is therefore that even if we strictly follow the thin shell formalism to cut and paste spacetimes, this does not guarantee that the resulting spacetime offers a physically reasonable background. 

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