Covariant Model for Spinning Classical Charge Distribution
Dylan MacDougall
Particles such as electrons require quantum mechanics to completely describe their evolution. To distinguish between quantum and classical effects in the evolution of a particle, a classical model for the particle is needed. This model must be in agreement with special relativity, as well as overcome the repulsive nature of the Coulomb force. This project attempts to accomplish this by modeling an elementary particle with spin using a classical, symmetric charge distribution which is rotating about an axis. As any configuration of electric charges is unstable in the absence of other forces, a second force field must be considered. We choose this second field as a Yukawa field, an interaction mediated by massive, spinless particles. We assure the fields are covariant by deriving them from an action principle. The forces acting on the distribution are then balanced to create a stable circular rotation of the distribution. Two charge distributions are considered; a dumbbell of two point charges and a continuous phase-space distribution of charge with cylindrical symmetry.
Spherical Symmetry in Teleparallel Gravity
Hudson Forance
Einstein's theory of general relativity(GR) is a very successful theory of gravity; however, it is not without its shortcomings. Since its inception in 1915, researchers have been met with various problems in the application of general relativity, primarily related to its prediction of singularities at the center of black holes, along with theoretical and observational discrepancies in the limiting cases of the $\Lambda CDM$ model. As such, modified frameworks of gravity are of growing interest in the field of cosmology, $f$(T)-type gravity is one such framework, where instead of using curvature to describe the relationship between matter, energy, and space-time in the universe, we use torsion as the fundamental source field for gravitational effects.
Expanding on previous work, I have found the local Lorentz transformation and the general purely inertial frame for a class of teleparallel geometries, specifically ones which are spherically symmetric. Starting with the spin connection for a general spherically symmetric teleparallel geometry, a system of matrix partial differential equations is established using the transformation laws for the spin connection. Solving these equations yields a transformation which can be applied to a generic spherically symmetric frame field, bringing it to a purely inertial(proper) frame, where the spin connection vanishes and so all inertial effects are absent. Additionally, physically relevant sub-cases are explored.
