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1. Quantization of spherically symmetric loop quantum gravity coupled to a scalar field and a clock: the asymptotic limit

   https://doi.org/10.1088/1361-6382/ad0b9d  

   Gambini, Rodolfo; Pullin, Jorge (November 2023, Classical and Quantum Gravity)

   Abstract We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian for the theory. The spherically symmetric context allows to carry out precise detailed calculations. Here we study the theory for regions of large values of the radial coordinate. This allows us to define in detail the vacuum of the theory and study its quantum states, yielding a quantum field theory on a quantum space time that makes contact with the usual treatment on classical space times. 

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2. Loop quantum gravity of a spherically symmetric scalar field coupled to gravity with a clock

   https://doi.org/10.1088/1361-6382/acc510  

   Gambini, Rodolfo; Pullin, Jorge (March 2023, Classical and Quantum Gravity)

   Abstract The inclusion of matter fields in spherically symmetric loop quantum gravity has proved problematic at the level of implementing the constraint algebra including the Hamiltonian constraint. Here we consider the system with the introduction of a clock. Using the abelianizaton technique we introduced in previous papers in the case of gravity coupled to matter, the system can be gauge fixed and rewritten in terms of a restricted set of dynamical variables that satisfy simple Poisson bracket relations. This creates a true Hamiltonian and therefore one bypasses the issue of the constraint algebra. We show how loop quantum gravity techniques may be applied for the vacuum case and show that the Hamiltonian system reproduces previous results for the physical space of states and the observables of a Schwarzchild black hole. 

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3. Emergent modified gravity

   https://doi.org/10.1088/1361-6382/ad36a8  

   Bojowald, Martin; Duque, Erick I (April 2024, Classical and Quantum Gravity)

   A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems are evaded by using a crucial and novel ingredient, allowing for fundamental fields of gravity distinct from an emergent space-time metric that provides a geometrical structure to all solutions. As specific examples, there are new expansion-shear couplings in cosmological models, a form of modified Newtonian dynamics can appear in a space-time covariant theory without introducing extra fields, and related effects help to make effective models of canonical quantum gravity fully consistent with general covariance. 

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4. 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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5. Quantum geometry and black holes

   Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge (January 2023, Handbook of Quantum Gravity",)

   Bambi, Cosimo; Modesto, Leonardo; Shapiro, Ilya (Ed.)

   We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so the Hamiltonian has an Abelian algebra with itself. We discuss basic and improved quantizations as is done in loop quantum cosmology. We discuss the use of parameterized Dirac observables to define operators associated with kinematical variables in the physical space of states, as a first step to introduce an operator associated with the space-time metric. We analyze the elimination of singularities and how they are replaced by extensions of the space-times. We discuss the charged case and potential observational consequences in quasinormal modes. We also analyze the covariance of the approach. Finally, we comment on other recent approaches of quantum black holes, including mini-superspaces motivated by loop quantum gravity. 

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