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It has been proposed by Bekenstein and others that the horizon area of a black hole conforms, upon quantization, to a discrete and uniformly spaced spectrum. In this paper, we consider the area spectrum for the highly non-trivial case of a…
We present and contrast two distinct ways of including extremal black holes in a Lorentzian Hamiltonian quantization of spherically symmetric Einstein-Maxwell theory. First, we formulate the classical Hamiltonian dynamics with boundary…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
The longstanding issue of general covariance in effective models of quantum gravity is addressed, which arises when canonical quantum gravity leads to a semiclassical model described by an effective Hamiltonian constraint. In the context of…
Several properties of canonical quantum gravity modify space-time structures, sometimes to the degree that no effective line elements exist to describe the geometry. An analysis of solutions, for instance in the context of black holes, then…
This review gives an introduction into problems, concepts and techniques when quantizing matter fields near black holes. The first part focusses on quantum fields in general curved space-times. The second part is devoted to a detailed…
We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains…
Acoustic spacetimes have been known to offer analogue models for black hole physics and cosmology. Within this context, aspects of analogue quantum field theories in curved spacetime are studied. In particular some new comments have been…
Simulation and experimental realization of acoustic black holes in analogue gravity systems have lead to a novel understanding of relevant phenomena such as Hawking radiation or superradiance. We explore here the possibility to use…
We obtain the Hawking spectrum by exponentiating a series of Feynman diagrams describing a scalar field scattering through a collapse background. Our approach is rooted in semiclassical methods of scattering amplitudes which have recently…
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on…
A pseudo-Riemannian manifold contains an inherent Hamiltonian structure within the symplectic manifold in the cotangent bundle corresponding to the metric. Using this structure, it is possible to define a Hamiltonian, which can be…
Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This…
The formalism of the horizon quantum mechanics is applied to electrically neutral and spherically symmetric black hole geometries emerging from coherent quantum states of gravity to compute the probability that the matter source is inside…
We develop a technique relating scalar fields with different masses in different conformally flat space-times. We apply this technique to the case of FRW space-times, with $k=\pm 1,0$, and discuss several examples. We also study various…
We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature…
We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy…
Kucha\v{r} has recently given a detailed analysis of the classical and quantum geometrodynamics of the Kruskal extension of the Schwarzschild black hole. In this paper we adapt Kucha\v{r}'s analysis to the exterior region of a Schwarzschild…
The familiar approach to quantum radiation following collapse to a black hole proceeds via Bogoliubov transformations, and yields probabilities for final outcomes. In our (complex) approach, we find quantum amplitudes, not just…
Loop Quantum Gravity (LQG) is a theory that proposes a way to model the behavior of the spacetime in situations where its atomic characteristic arises. Among these situations, the spacetime behavior near the Big Bang or black hole's…