Related papers: The curious case of operators with spectral densit…
We show that, apart from the usual area operator of non-perturbative quantum gravity, there exists another, closely related, operator that measures areas of surfaces. Both corresponding classical expressions yield the area. Quantum…
The adiabatic invariant nature of black hole horizon area in classical gravity suggests that in quantum theory the corresponding operator has a discrete spectrum. I here develop further an algebraic approach to black hole quantization which…
The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…
Suppose that there is a quantum operator that describes the horizon area of a black hole. Then what would be the form of the ensuing quantum spectrum? In this regard, it has been conjectured that the characteristic frequencies of the black…
Despite all the analogies with "usual random" models, tight binding operators for quasicrystals exhibit a feature which clearly distinguishes them from the former: the integrated density of states may be discontinuous. This phenomenon is…
In some respects the black hole plays the same role in gravitation that the atom played in the nascent quantum mechanics. This analogy suggests that black hole mass $M$ might have a discrete spectrum. I review the physical arguments for the…
We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite…
Using a recently developed quantization of spherically symmetric gravity coupled to a scalar field, we give a construction of null expansion operators that allow a definition of general, fully dynamical quantum black holes. These operators…
It has been argued by several authors, using different formalisms, that the quantum mechanical spectrum of black hole horizon area is discrete and uniformly spaced. Recently it was shown that two such approaches, namely the one involving…
We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this…
Bekenstein proposed that the spectrum of horizon area of quantized black holes must be discrete and uniformly spaced. We examine this proposal in the context of spherically symmetric charged black holes in a general class of gravity…
In this Letter, we study black hole area quantization in the context of gravitational wave physics. It was recently argued that black hole area quantization could be a mechanism to produce so-called echoes as well as characteristic…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
When a classical black hole is perturbed, its relaxation is governed by a set of quasinormal modes with complex frequencies \omega= \omega_R+i\omega_I. We show that this behavior is the same as that of a collection of damped harmonic…
We show that the black hole laser effect discovered by Corley & Jacobson should be described in terms of frequency eigenmodes that are spatially bound. The spectrum contains a discrete and finite set of complex frequency modes which appear…
Simple arguments related to the entropy of black holes strongly constrain the spectrum of the area operator for a Schwarzschild black hole in loop quantum gravity. In particular, this spectrum is fixed completely by the assumption that the…
We show how the spectrum of normal discrete short-range infinite-volume operators can be approximated with two-sided error control using only data from finite-sized local patches. As a corollary, we prove the computability of the spectrum…
The enumeration of black hole entropy in candidate theories of quantum gravity utilises the quantum properties of microstates residing on the black hole horizon. For example, in Loop Quantum Gravity, the computation of entropy is based on…
We study fundamental spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…