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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. Spherically symmetric random permutations

   https://doi.org/10.1002/rsa.20847  

   Gnedin, Alexander; Gorin, Vadim (March 2019, Random Structures & Algorithms)

   We consider random permutations which are spherically symmetric with respect to a metric on the symmetric groupS_nand are consistent asnvaries. The extreme infinitely spherically symmetric permutation‐valued processes are identified for the Hamming, Kendall‐tau and Cayley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity. 

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3. 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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4. Strong cosmic censorship in the presence of matter: the decisive effect of horizon oscillations on the black hole interior geometry

   https://doi.org/10.2140/apde.2024.17.1501  

   Kehle, Christoph; Van_de_Moortel, Maxime (June 2024, Analysis & PDE)

   Motivated by the strong cosmic censorship conjecture in the presence of matter, we study the Einstein equations coupled with a charged/massive scalar field with spherically symmetric characteristic data relaxing to a Reissner–Nordström event horizon. Contrary to the vacuum case, the relaxation rate is conjectured to be slow (nonintegrable), opening the possibility that the matter fields and the metric coefficients blow up in amplitude at the Cauchy horizon, not just in energy. We show that whether this blow-up in amplitude occurs or not depends on a novel oscillation condition on the event horizon which determines whether or not a resonance is excited dynamically. If the oscillation condition is satisfied, then the resonance is not excited and we show boundedness and continuous extendibility of the matter fields and the metric across the Cauchy horizon. If the oscillation condition is violated, then by the combined effect of slow decay and the resonance being excited, we show that the massive uncharged scalar field blows up in amplitude. In a companion paper, we will show that in that case a novel null contraction singularity forms at the Cauchy horizon, across which the metric is not continuously extendible in the usual sense. Heuristic arguments in the physics literature indicate that the oscillation condition should be satisfied generically on the event horizon. If these heuristics are true, then our result falsifies the continuous-formulation of strong cosmic censorship by means of oscillation. 

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5. Non-spherical dark matter structures detection

   https://doi.org/10.1088/1475-7516/2022/03/049  

   Loizeau, Nicolas; Farrar, Glennys R. (March 2022, Journal of Cosmology and Astroparticle Physics)

   Abstract A rotation curve inequality that holds for spherically symmetric mass distributions is derived, and tested against the SPARC galaxy rotation curves dataset. We identify several Galaxies, e.g. NGC7793 and UGC11557, which are candidates for hosting non-spherical dark matter structures that could be detected by more precise measurements. 

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