Related papers: The Area Spectrum in Quantum Gravity
Quantum fluctuations of the spacetime metric induce an uncertainty in the horizon area of a black hole. Working in linearized quantum gravity, we derive the variance in the area of a four-dimensional Schwarzschild black hole from the…
Beginning with Bekenstein, many authors have considered a uniformly spaced discrete quantum spectrum for black hole horizon area. It is also believed that the huge degeneracy of these area levels corresponds to the notion of black hole…
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…
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…
The recent speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization law is confirmed. We exclusively utilize the period of motion of an outgoing wave, which is shown to be related to the…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely…
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 propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture…
A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric. It is used to continue the exploration of the quantum Riemannian geometry. Operators corresponding to…
A `black hole sector' of non-perturbative canonical quantum gravity is introduced. The quantum black hole degrees of freedom are shown to be described by a Chern-Simons field theory on the horizon. It is shown that the entropy of a large…
The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity - the length operator. We describe its quantum geometrical meaning and derive…
The problem of time operator in quantum mechanics is revisited. The unsharp measurement model for quantum time based on the dynamical system-clock interaction, is studied. Our analysis shows that the problem of the quantum time operator…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
We study the spectrum of the length and area operators in Lorentzian loop quantum gravity, in 2+1 spacetime dimensions. We find that the spectrum of spacelike intervals is continuous, whereas the spectrum of timelike intervals is discrete.…
The entropy-area spectrum of a black hole has been a long-standing and unsolved problem. Based on a recent methodology introduced by two of the authors, for the black hole radiation (Hawking effect) as tunneling effect, we obtain the…
We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its matrix elements, it is possible for the first time to treat…
We compare two area spectra proposed in loop quantum gravity in different approaches to compute the entropy of the Schwarzschild black hole. We describe the black hole in general microcanonical and canonical area ensembles for these…
We show that in the Snyder space the area of the disc and of the sphere can be quantized. It is also shown that the area spectrum of the sphere can be related to the Bekenstein conjecture for the area spectrum of a black hole horizon.
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…