Related papers: Quantum singularities in spherically symmetric, co…
We consider a general non-linear sigma model coupled to Einstein gravity and show that in spherical symmetry and for a simple realization of self-similarity, the spacetime can be completely determined. We also examine some more specific…
Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time dependent…
Brane-world singularities are analysed, emphasizing the case of supergravity in singular spaces where the singularity puzzle is naturally resolved. These naked singularities are either time-like or null, corresponding to the finite or…
We investigate static spherically symmetric vacuum solutions in the IR limit of projectable nonrelativistic quantum gravity, including the renormalisable quantum gravity recently proposed by Ho\v{r}ava. It is found that the projectability…
It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
Based on modifications inspired from loop quantum gravity (LQG), spherically symmetric models have recently been explored to understand the resolution of classical singularities and the fate of the spacetime beyond. While such…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
We present an effective theory to describe the quantization of spherically symmetric vacuum in loop quantum gravity. We include anomaly-free holonomy corrections through a canonical transformation of the Hamiltonian of general relativity,…
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…
According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal…
The Klein-Gordon equations were recently solved in general relativity for the case of a plane-symmetric static massless scalar field with cosmological constant. By analytic continuation, time-dependent solutions can be obtained that…
We use the formulation of the quantum mechanics of first quantized Klein-Gordon fields given in the first of this series of papers to study relativistic coherent states. In particular, we offer an explicit construction of coherent states…
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 consider a model of Quantum Gravity phenomenology, based on the idea that space-time may have some unknown granular structure that respects the Lorentz symmetry. The proposal involves non-trivial couplings of curvature to matter fields…
A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.
We investigate canonical quantization of a general spherically symmetric spacetimes with a massless scalar-field source and examine the associated constraint algebra. The spacetimes are quantized using Dirac's quantization method for…