Related papers: Spacetime Symmetries and Kepler's Third Law
We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The noncovariant spin formalism is crucial for the…
We study a limit of the Kerr-(A)dS spacetime in a general dimension where an arbitrary number of its rotational parameters is set equal. The resulting metric after the limit formally splits into two parts - the first part has the form of…
Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to…
The equations of motion of massive test particles near Kerr black holes are separable in Boyer-Lindquist coordinates, as established by Carter. This separability, however, is lost when the particles are endowed with classical spin. We show…
The equations of general relativity in the form of timelike and null geodesics that describe motion of test particles and photons in Kerr spacetime are solved exactly including the contribution from the cosmological constant. We then…
Some basic theorems on Killing vector fields are reviewed. In particular, the topic of a constant-curvature space is examined. A detailed proof is given for a theorem describing the most general form of the metric of a homogeneous isotropic…
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…
The automorphism invariant theory of Crawford[J. Math. Phys. 35, 2701 (1994)] has show great promise, however its application is limited by the paradigm to the domain of spin space. Our conjecture is that there is a broader principle at…
To incorporate quantum nonlocality into general relativity, we propose that the preparation and measurement of a quantum system are simultaneous events. To make progress in realizing this proposal, we introduce a spacetime geometry that is…
We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…
We consider the coupling between massive and spinning particles and three dimensional gravity. This allows us to construct geometric operators (distances between particles) as Dirac observables. We quantize the system a la loop quantum…
Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology…
We consider various generalizations of the Kepler problem to three-dimensional sphere $S^3$, a compact space of constant curvature. These generalizations include, among other things, addition of a spherical analog of the magnetic monopole…
A quantum sl(2,R) coalgebra (with deformation parameter z) is shown to underly the construction of superintegrable Kepler potentials on 3D spaces of variable and constant curvature, that include the classical spherical, hyperbolic and…
A novel but elementary geometric construction produces on the seven-dimensional manifold of rotated spheres in Euclidean three-space a finslerian geometry whose geodesics are interpreted as the paths of free, spinning, spherical particles…
Classical-particle trajectories are calculated for the static Einstein universe without requiring that the 3-space be closed and curved. Freely-moving test particles are found to return to their starting positions because of strong…
We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable…
The gravitational field exterior respectively interior to a spherically symmetric, isolated body made of perfect fluid is examined within the quasi-metric framework (QMF). It is required that the gravitational field is "metrically static",…