Date of Award:
Doctor of Philosophy (PhD)
Charles G. Torre
Charles G. Torre
James T. Wheeler
Mark E. Fels
You might have heard of Einstein’s theory of General relativity (GR): it is the one where mass and energy curve the fabric of spacetime to create gravity. This is the major theory which allows communication through satellites and our GPS to work too! Wormholes have interested me, but there are some issues about forming them in GR. Interestingly enough, elementary particles are also characterized by their spin in the standard model. However, intrinsic spin is nowhere geometrically coupled to the geometry of spacetime in Einstein’s theory. Later, Élie Cartan, Dennis Sciama, and Tom Kibble all flushed out adding different aspects of Spin into GR making a new theory called Einstein-Cartan-Sciama-Kibble (ECSK) theory where spin is linked to the torsion tensor of Cartan. This addition of spin according to several articles allows for wormholes without any invocation of exotic matter (negative mass). There’s the background! This dissertation breaks apart ECSK theory into observable through the use of the Lorentz group, encompassing time dilation and rotations. The consequences are that we can find new physics through the use of these tools which correspond to structures in spacetime. Then by forming combinations of these objects (think x2) we can further analyze the geometrical structures and get a handle on what is happening physically! Computer tools in the Maple software package have been developed to expedite calculation on several ECSK problems. Together these tools form an ECSK toolkit which corresponds to the ideas used by Petrov, Plebanski, Segre, and Penrose (PPSP) to classify structures in GR.
Leiter, Joshua James, "A Classification of Tensors in ECSK Theory" (2023). All Graduate Theses and Dissertations. 8766.
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Code for this dissertation can be found here: https://digitalcommons.usu.edu/phys_stures/39/