Related papers: Quantum geometry and black holes
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
Over the last three years, a number of fundamental issues in quantum gravity were addressed in the framework of quantum geometry, discussed extensively by John Baez in this conference. In particular, these include: A statistical mechanical…
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner…
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…
We continue the study of spherically symmetric vacuum space-times in loop quantum gravity by treating the interior of a black hole. We start from a midi-superspace approach, but a simple gauge fixing leads to a Kantowski--Sachs form for the…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…
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…
Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric…
Symmetric states are defined in the kinematical sector of loop quantum gravity and applied to spherical symmetry and homogeneity. Consequences for the physics of black holes and cosmology are discussed.
We review our recent proposal of a method to extend the quantization of spherically symmetric isolated horizons, a seminal result of loop quantum gravity, to a phase space containing horizons of arbitrary geometry. Although the details of…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
We study the "improved dynamics" for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou {\em et al.} in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the…
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and 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…
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…
We elaborate on the Ashtekar's formalism for spherically symmetric midisuperspaces and, for loop quantization, propound a new quantization scheme which yields a graph-preserving Hamiltonian constraint operator and by which one can impose…