Related papers: Ascribing quantum system to Schwarzschild spacetim…
We study the quantum motion of null shells in the quantum space-time of a black hole in loop quantum gravity. We treat the shells as test fields and use an effective dynamics for the propagation equations. The shells propagate through the…
In a recent paper by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in…
This thesis contains an analysis of the problem of time in quantum cosmology and its application to a cosmological minisuperspace model. In the first part, we introduce the problem of time and the theoretical foundations. In the second…
We suggest a scheme for considering the quantum correction of the gravitational constant. In the model, the gravitational constant originates from a coupling of the gravitational field with a scalar field. In this paper, we show that if the…
We show that the average trajectories of relativistic quantum particles in Schwarzschild spacetime, obtained via quantum mechanical weak measurements of momentum and energy, are equivalent to the predicted flow lines of probability current…
We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian…
Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
A class of $k$-Essence cosmological models, with a power law kinetic term, is quantised in the mini-superspace. It is shown that for a specific configuration, corresponding to a pressureless fluid, a Schr\"odinger-type equation is obtained…
We explore a theory of large-scale gravitational quantization, using the general relativistic Hamilton-Jacobi equation to create quantization conditions via a new scalar wave equation dependent upon the total mass and the total vector…
In this continuation paper, we apply the general relativistic quantum theory for one particle systems, derived in paper II of this series, to a simple problem: the quantum Schwartzchild problem, where one particle of mass {\it m% }…
The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches.…
We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie…
We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
The formation of naked singularities in $2+1-$ dimensional power - law spacetimes in linear Einstein-Maxwell and Einstein-scalar theories sourced by azimuthally symmetric electric field and a self-interacting real scalar field respectively,…
Simple classical mechanical systems and solution spaces of classical field theories involve singularities. In certain situations these singularities can be understood in terms of stratified Kaehler spaces. We give an overview of a research…
In this work we study the spectral dimensionality of spacetime around a radiating Schwarzschild black hole using a recently introduced formalism of quantum gravity, where the alterations of the gravitational field produced by the radiation…
The precision of optical atomic clocks is approaching a regime where they resolve gravitational time dilation on smaller scales than their own extensions. Hence, an accurate description of quantum clocks has to take their spatial extension…
There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star,…