Browsing by Author "Pollney, Denis"

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    Classical, quantum and numerical aspects of modified theories of gravity
    (2024) Beckering Vinckers, Ulrich Karoo; De La Cruz, Dombriz Alvaro; Mazumdar, Anupam; Pollney, Denis
    In this thesis, we examine some specific aspects of two classes of modified gravity theories: ghostfree infinite-derivative gravity and so-called f(R) gravity. Regarding the former, we consider the four-dimensional theory at the level of the quadratic action and study the single graviton exchange of two massive spin-0 particles. We derive the corresponding gravitational potential energy for the non-static case and show that the quantum correction of the local theory, which is in the form of a Dirac delta function, is smeared out in the non-local theory. It is also shown that the gravitational potential energy associated with the self-interaction of the individual particles is finite. We then examine the quantumgravitational entanglement of two test masses that undergo a spatial splitting that is orthogonal to their separation. For such a set-up, we compute the concurrence and von Neumann entropy for the entanglement and show that an increase in the length scale of nonlocality leads to a decrease in both of the aforementioned quantities. Our attention is then turned to two specific two-dimensional dilaton gravity models; namely the Spherically-Reduced Gravity (SRG) and the Callan-Giddings-Harvey-Strominger (CGHS) theories. The quadratic action for each theory is derived and diagonalised in order to construct ghost-free infinite-derivative modifications. In the case of the SRG theory, we make use of the Schwarzschild-type gauge whereas, for the CGHS theory, we impose the conformal gauge. For each of the two local theories, we construct appropriate source actions that can be used to generate their respective linearised black-hole solutions. We then make use of the same source actions in the linearised non-local theories and obtain non-local modifications to the aforesaid solutions. Lastly, we consider the application of numerical relativity techniques to f(R) gravity models. It is well-known that the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) modification of the Arnowitt-Deser-Misner formulation of General Relativity is suitable for the construction of numerical relativity codes. While a BSSN-like formulation for f(R) gravity exists, it is constructed with Cartesian coordinates in mind. In this thesis, we generalise the formalism to accommodate arbitrary coordinates and then impose spherical symmetry. The description of a numerical relativity code for the Starobinsky gravity model based on this formalism is given before considering a number of scenarios. We first perform the evolution of Schwarzschild Einstein-Rosen bridge initial data using the fourth-order Runge-Kutta method as well as the evolution of a gauge pulse in flat space using the Partially-Implicit-Runge-Kutta scheme. These two cases serve as tests for our code and our results are compared with those presented in the literature. Then, we perform the evolution of a massless scalar field in the context of the Starobinsky gravity model and show that damped oscillations arise for subcritical simulations.
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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.