Physics Student Research
Document Type
Other
Author ORCID Identifier
Joshua James Leiter https://orcid.org/0000-0001-9248-7802
Publication Date
4-14-2023
Abstract
This dissertation presents a Petrov/Plebanski/Segre/Algebraic (PPSA) classification scheme for both the curvature and torsion tensors in Einstein-Cartan-Sciama-Kibble theory (ECSK); additionally the work includes a software package in Maple with computational and PPSA classification tools. Six different solutions are classified using the new software tools developed. We also present a new boundary term for ECSK-NMC scalar theory to ensure Dirichlet boundary conditions. New work completed includes the decomposition of an arbitrary 4th rank tensor under SO (p, q), equivalent SL (2, C) irreducible spinor decompositions of arbitrary 3rd and 4th rank tensors. We provide new proofs that the corresponding spinors are the irreducible components in the SL (2, C) decomposition of 3rd and 4th rank tensors using Maple. Additionally, we provide an algebraic decomposition of the torsion spinors, an algorithm determining their algebraic decomposition, an ECSK- PPSA classification for the curvature tensor, and finally the Gibbons-Hawking-York (GHY) - ECSK - Non-Minimally-Coupled (NMC) scalar field boundary term such that the metric variation vanishes on the boundary without any need to constrain the normal derivatives of the variation of the metric.
Referenced by
A Classification of Tensors in ECSK Theory [dissertation]
Recommended Citation
Leiter, Joshua James and Torre, Charles G., "For the Dissertation: A Classification of Tensors in ECSK Theory" (2023). Physics Student Research. Paper 39.
https://digitalcommons.usu.edu/phys_stures/39
Comments
These files are used to illustrate the procedures developed for the dissertation: "A CLASSIFICATION OF TENSORS IN ECSK THEORY". Their proper use should become apparent when the Maple files are examined. Additionally all procedures presented in the modules are compatible with the "DifferentialGeometry" package constructed by Ian Anderson and Charles Torre. Maple and the USU DifferentialGeometry Package are required to use these procedures.
Copyright [2023] [Joshua James Leiter] Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.