Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes

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dc.contributor.advisorDe La Cruz-Dombriz, Alvaro
dc.contributor.advisorPollney, Denis
dc.contributor.authorBeckering Vinckers, Ulrich Karoo
dc.date.accessioned2021-07-20T09:05:46Z
dc.date.available2021-07-20T09:05:46Z
dc.date.issued2021
dc.date.updated2021-07-15T10:24:44Z
dc.description.abstractIn this thesis, we study gravitational theories for which the natural choice of an affine connection is metric compatible while not being symmetric. More specifically, we study gravitational theories constructed on the Riemann-Cartan and Weitzenböck space-times. Firstly, we outline the mathematical notions needed to construct a definition of space-time. Following this, we introduce the space-time definitions to be made use of throughout this thesis. We then discuss the notions of extremal and auto-parallel curves on the Riemann-Cartan space-time. It is noted that test particles follow extremal curves which are auto-parallel curves of the LeviCivita connection. Therefore, one must turn to the standard, torsion-free Raychaudhuri equation when studying the focusing conditions that arise in theories constructed on the Riemann-Cartan or Weitzenböck space-times. Once we have introduced the definitions of the relevant space-times, we move on to review some of the gravitational theories that involve non-vanishing torsion. We first review the Einstein-Cartan theory and two of its modifications. We then review the so-called f(T) theories of gravity before discussing the focusing conditions that arise in this context. By making use of the f(T) field equations together with the torsion-free Raychaudhuri equation, we derive for the first time the f(T) focusing conditions for a one-parameter dependent congruence of timelike auto-parallel curves of the LeviCivita connection. We then study these focusing conditions for three bi-parametric cosmological models. Finally, we turn our attention back to the Einstein-Cartan theory and derive the Arnowitt-DeserMisner formulation of this theory. By making use of this formulation, we derive for the first time the Generalised-Baumgarte-Shapiro-Shibata-Nakamura formulation of the Einstein-Cartan theory. We then consider the case of a vacuum in spherical symmetry and construct a 1-dimensional code to evolve the system numerically. We leave the inclusion of torsion into this code as the subject for future work.
dc.identifier.apacitationBeckering Vinckers, U. K. (2021). <i>Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes</i>. (). ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/33637en_ZA
dc.identifier.chicagocitationBeckering Vinckers, Ulrich Karoo. <i>"Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes."</i> ., ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2021. http://hdl.handle.net/11427/33637en_ZA
dc.identifier.citationBeckering Vinckers, U.K. 2021. Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes. . ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/33637en_ZA
dc.identifier.ris TY - Master Thesis AU - Beckering Vinckers, Ulrich Karoo AB - In this thesis, we study gravitational theories for which the natural choice of an affine connection is metric compatible while not being symmetric. More specifically, we study gravitational theories constructed on the Riemann-Cartan and Weitzenböck space-times. Firstly, we outline the mathematical notions needed to construct a definition of space-time. Following this, we introduce the space-time definitions to be made use of throughout this thesis. We then discuss the notions of extremal and auto-parallel curves on the Riemann-Cartan space-time. It is noted that test particles follow extremal curves which are auto-parallel curves of the LeviCivita connection. Therefore, one must turn to the standard, torsion-free Raychaudhuri equation when studying the focusing conditions that arise in theories constructed on the Riemann-Cartan or Weitzenböck space-times. Once we have introduced the definitions of the relevant space-times, we move on to review some of the gravitational theories that involve non-vanishing torsion. We first review the Einstein-Cartan theory and two of its modifications. We then review the so-called f(T) theories of gravity before discussing the focusing conditions that arise in this context. By making use of the f(T) field equations together with the torsion-free Raychaudhuri equation, we derive for the first time the f(T) focusing conditions for a one-parameter dependent congruence of timelike auto-parallel curves of the LeviCivita connection. We then study these focusing conditions for three bi-parametric cosmological models. Finally, we turn our attention back to the Einstein-Cartan theory and derive the Arnowitt-DeserMisner formulation of this theory. By making use of this formulation, we derive for the first time the Generalised-Baumgarte-Shapiro-Shibata-Nakamura formulation of the Einstein-Cartan theory. We then consider the case of a vacuum in spherical symmetry and construct a 1-dimensional code to evolve the system numerically. We leave the inclusion of torsion into this code as the subject for future work. DA - 2021_ DB - OpenUCT DP - University of Cape Town KW - Mathematics and Applied Mathematics LK - https://open.uct.ac.za PY - 2021 T1 - Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes TI - Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes UR - http://hdl.handle.net/11427/33637 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/33637
dc.identifier.vancouvercitationBeckering Vinckers UK. Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes. []. ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2021 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/33637en_ZA
dc.language.rfc3066eng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.subjectMathematics and Applied Mathematics
dc.titleUniverse phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationlevelMSc
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