We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.

We use the combinatorial and number-theoretical methods developed in previous works by the authors to study black hole entropy in the new proposal put forth by Engle, Noui, and Pérez. Specifically, we give the generating functions relevant for the computation of the entropy and use them to derive its asymptotic behavior, including the value of the Immirzi parameter and the coefficient of the logarithmic correction.

We show that, for space-times with inner boundaries, there exists a natural area operator different from the standard one used in loop quantum gravity. This new flux-area operator has equidistant eigenvalues. We discuss the consequences of substituting the standard area operator in the Ashtekar-Baez-Corichi-Krasnov definition of black hole entropy by the new one. Our choice simplifies the definition of the entropy and allows us to consider only those areas that coincide with the one defined by the value of the level of the Chern-Simons theory describing the horizon degrees of freedom. We give a prescription to count the number of relevant horizon states by using spin components and obtain exact expressions for the black hole entropy. Finally we derive its asymptotic behavior, discuss several issues related to the compatibility of our results with the Bekenstein-Hawking area law and the relation with Schwarzschild quasinormal modes.

We introduce an iterative method to univocally determine the adiabatic expansion of the modes of Dirac fields in spatially homogeneous external backgrounds. We overcome the ambiguities found in previous studies and use this new procedure to improve the adiabatic regularization/renormalization scheme. We provide details on the application of the method for Dirac fields living in a four-dimensional Friedmann-Lemaître-Robertson-Walker spacetime with a Yukawa coupling to an external scalar field. We check the consistency of our proposal by working out the conformal anomaly. We also analyze a two-dimensional Dirac field in Minkowski space coupled to a homogeneous electric field and reproduce the known results on the axial anomaly. The adiabatic expansion of the modes given here can be used to properly characterize the allowed physical states of the Dirac fields in the above external backgrounds.

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an i

The goal of this paper is to propose and discuss a practical way to implement the Dirac algorithm for constrained field models defined on spatial regions with boundaries . Our method is inspired in the geometric viewpoint developed by Gotay, Nester, and Hinds (GNH) to deal with singular Hamiltonian systems. We pay special attention to the specific issues raised by the presence of boundaries and provide a number of significant examples—among them field theories related to general relativity—to illustrate the main features of our approach.