Related papers: Definition and classification of singularities in …
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
Quantum gravity--the marriage of quantum physics with general relativity--is bound to contain deep and important lessons for the nature of physical time. Some of these lessons shall be canvassed here, particularly as they arise from quantum…
This paper gives an elementary introduction to some of the conceptual problems of quantum cosmology. Contents: 1. Why quantum cosmology? 2. Time in quantum gravity 3.Decoherence and the recovery of the Schrodinger equation 4. The direction…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
Key issues of classical and quantum strings in gravitational plane waves, shock waves and spacetime singularities are synthetically understood. This includes the string mass and mode number excitations, energy-momentum tensor, scattering…
We propose a new notion of singularity in General Relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a spacetime has a volume singularity if there exist points…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
General relativity predicts its own demise at singularities, but also appears to conveniently shield itself from the catastrophic consequences of such singularities, making them safe. For instance, if strong cosmic censorship were…
It has been claimed in a recent paper \cite{bbfhd12} that sudden singularities will survive in semiclassical gravity. This issue is here carefully reviewed, pointing out that such conclusion, even if valid under some specific conditions,…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
General relativity describes the gravitational field geometrically and in a self-interacting way because it couples to all forms of energy, including its own. Both features make finding a quantum theory difficult, yet it is important in the…
In quantum gravity there is no notion of absolute time. Like all other quantities in the theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a…
Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change,…
We study the classical and quantum theory of spherically symmetric spacetimes with scalar field coupling in general relativity. We utilise the canonical formalism of geometrodynamics adapted to the Painleve-Gullstrand coordinates, and…
We consider a global quantum system (the "Universe") satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a model of 3+1 dimensional,…
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic…
In view of the enormous difficulties we seem to face in quantizing general relativity, we should perhaps consider the possibility that gravity is a fundamentally classical interaction. Theoretical arguments against such mixed…
The formation of a naked singularity in a model of f(R) gravity having as source a linear electromagnetic field is considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell equations are used…
Several definitions for the average local value and local variance of a quantum observable are examined and compared with their classical counterparts. An explicit way to construct an infinite number of these quantities is provided. It is…
It is plausible that quantum gravity effects may lead us to a description of Nature beyond the framework of special relativity. In this case, either the relativity principle is broken or it is maintained. These two scenarios (a violation or…