Browsing by Author "De La Cruz-Dombriz, Alvaro"

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    New effective theories of gravitation and their phenomenological consequences
    (University of Cape Town, 2020) Maldonado Torralba, Francisco José; De La Cruz-Dombriz, Alvaro; Mazumdar, Anupam
    The objective of this Thesis is to explore Poincaré Gauge theories of gravity and expose some contributions to this field, which are detailed below. Moreover, a novel ultraviolet non-local extension of this theory shall be provided, and it will be shown that it can be ghost- and singularity-free at the linear level. First, we introduce some fundamentals of differential geometry, base of any gravitational theory. We then establish that the affine structure and the metric of the spacetime are not generally related, and that there is no physical reason to impose a certain affine connection to the gravitational theory. We review the importance of gauge symmetries in Physics and construct the quadratic Lagrangian of Poincaré Gauge gravity by requiring that the gravitational theorymust be invariant under local Poincaré transformations. We study the stability of the quadratic Poincaré Gauge Lagrangian, and prove that only the two scalar degrees of freedom (one scalar and one pseudo-scalar) can propagate without introducing pathologies. We provide extensive details on the scalar, pseudo-scalar, and bi-scalar theories. Moreover, we suggest how to extend the quadratic Poincaré Gauge Lagrangian so that more modes can propagate safely. We then proceed to explore some interesting phenomenology of Poincaré Gauge theories. Herein, we calculate how fermionic particles move in spacetimes endowed with a nonsymmetric connection at first order in the WKB approximation. Afterwards, we use this result in a particular black-hole solution of Poincaré Gauge gravity, showing that measurable differences between the trajectories of a fermion and a boson can be observed. Motivated by this fact, we studied the singularity theorems in theories with torsion, to see if this non-geodesical behaviour can lead to the avoidance of singularities. Nevertheless, we prove that this is not possible provided that the conditions for the appearance of black holes of any co-dimension are met. In order to see which kind Black Hole solutions we can expect in Poincaré Gauge theories, we study Birkhoff and no-hair theorems under physically relevant conditions. Finally, we propose an ultraviolet extension of Poincaré Gauge theories by introducing non-local (infinite derivatives) terms into the action, which can ameliorate the singular behaviour at large energies. We find solutions of this theory at the linear level, and prove that such solutions are ghost- and singularity-free. We also find new features that are not present in metric Infinite Derivative Gravity.
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    Stability and gravitational collapse in extended theories of gravity: from singularities to bouncing scenarios
    (2019) Hurgobin, Kirtika Juhi; De La Cruz-Dombriz, Alvaro
    Einstein theory of General Relativity was well adapted and accepted until limitations in the form of an unexplained form of energy, referred today as Dark Energy, were observed. For this reason, modifications to the standard Theory of General Relativity were proposed: the so-called f(R) theories. In this dissertation, after a passage on the generalities of cosmology, we use the metric formalism technique to derive the field equations for the general f(R) function. Thereafter we analyse and check the solutions proposed in [85] for the quadratic model in f(R) gravity, for spherically symmetric and static neutron stars, using two different viable equations of state. We also check the accuracy of our code through a forward-backward integration technique, to show that in both directions, we obtain the same results. We then perform a thorough analysis in the case of f(R) = R1+ models. Results will show that for a negative value, we have non-Schwarzschild, but asymptotically flat solutions, for which we can use the backward integration technique to retrieve the solutions from the forward integration. However, for the case of positive values, we will show the existence of horizons, which deny us the possibility of using the backward integration technique. One of the aims of this thesis is to check, through the backward integration technique that we developed, whether the exact exterior solutions proposed in [86], are indeed realistic solutions for neutron stars. We will see that for some cases, we do have realistic profiles, while for some others, although solutions exist, they are rejected due to their disagreement with the equation of state used therein.
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    Universe phenomenology as understood from gravitational theories with non-vanishing torsion: cosmology and black holes
    (2021) Beckering Vinckers, Ulrich Karoo; De La Cruz-Dombriz, Alvaro; Pollney, Denis
    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.