Towards a new spacetime paradigm : Gauge symmetries and post-Riemann geometries in gravitation

In this thesis the geometrical methods and symmetry principles in gravitation are explored motivating a new perspective into the spacetime paradigm. The effects of post-Riemann spacetime geometries with torsion are studied in applications to fundamental fermionic and bosonic fields, cosmology, astrophysics and gravitational waves. The physical implications and related phenomenological considerations of this study are addressed, and the fundamental ideas related to spacetime physics, motivated by geometrical methods and symmetry principles, are also discussed in the context of the possible routes towards a new spacetime paradigm in gravitation and unified field theories. We explore the analogies between the gauge approach to gravity and the pre-metric approach to electrodynamics, within the exterior calculus of forms. These analogies are developed, reinforcing the hypothesis of the primacy of the conformal structure over the metric structure. Since the conformal symmetries seem to be broken symmetries in nature, the Poincar´e gauge theories of gravity (PGTG) are taken into consideration. These presuppose a Riemann-Cartan (RC) spacetime geometry with curvature and torsion and motivate the search for torsion effects in physical systems. We study both minimal and non-minimal couplings of fermionic spinors to the background torsion and find changes in the energy levels (in the flat spacetime limit), including parity breaking effects. The Einstein-Cartan-Dirac-Maxwell theory is explored including its cosmological applications. The presence of minimal couplings to torsion induces non-linearities and non-minimal couplings in the matter fields dynamics and the resulting cosmological model is non-singular, including early and future bounces, early acceleration and torsion induced dark-energy due to fermionic vacuum condensates. Some potential astrophysical applications due to the torsion interaction with fermionic and bosonic fields are also considered as well as the effects of curvature in electromagnetic fields, including the extensions with inhomogeneous and anisotropic constitutive electromagnetic relations that respect the local isometries. In this context, the Parametrized Post-Newtonian (PPN) formalism is also implemented, making a bridge with the testing of different gravity theories. The effects of torsion are also analysed in gravitational wave (GW) physics, following the perturbations of a RC spacetime and in the field equations of a specific quadratic PGTG. The gravitational wave effects into electromagnetic fields are also studied with potential applications for non-standard detectors, which in principle could be extended for theories beyond GR, searches of extra polarizations and extra degrees of freedom

Geometrical methods in electromagnetism and gravitation: gravitoelectromagnetism and gravity with torsion (with cosmological applications)

Tese de mestrado em Física, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2012Principais motivações que orientam a linha de investigação na qual a tese se insere: - Aprofundar o estudo da relação íntima entre geometria e física; - Estudar as analogias e o acoplamento entre gravidade e electromagnetismo usando métodos geométricos, compreendendo a possibilidade de importantes aplicações teóricas e tecnológicas, podendo mesmo ser relevante para a astrofísica, a cosmologia e, eventualmente, no caminho para uma teoria consistente da gravidade quântica; - Estudar o gravitoelectromagnetismo e suas aplicações astrofísicas e eventualmente tecnológicas; - Explorar a noção de torsão em geometria diferencial e sua importância em física, nomeadamente no âmbito das teorias de gravitação. Enquadramento geral e tópicos principais da dissertação. Relação entre geometria e Natureza - relação entre geometria e física. • Importância dos métodos geométricos no estudo do campo eletromagnético e da gravidade e na exploração das analogias e acoplamento entre estas duas interações: • Axiomática do electromagnetismo; • Gravitoelectromagnetismo; • Acoplamento entre gravidade e electromagnetismo; • Gravidade com torsão: - Relevância teórica. Diferentes modelos; - Alguns modelos cosmológicos; - Exploração das analogias entre gravidade e electromagnetismo; - Testes experimentais. A questão da interpretação do papel das estruturas geométricas do espaço-tempo em física é abordada, realçando algumas reflexões relacionadas com a geometrização da física, motivadas pelo estudo das analogias e acoplamento entre gravidade e electromagnetismo. Neste âmbito a noção da ontologia física do espaço-tempo é brevemente abordada na sua conexão com as teorias unificadas.Although this work contains many personal investigations, interpretations and ideas, it was mainly constructed as a review compilation on several selected topics concerning the electromagnetic and gravitational studies using geometrical methods. The selected topics and their sources reflect the author’s interests and were compiled together and organized into a single framework in order to construct a meaningful and solid line of research on the related topics of gravitation and electromagnetism. One could say that this project fits within the wider scientific arena for research on the relation between geometry and physics and the nature of space and time. Some of the topics addressed, such as the coupling of gravity and electromagnetism, gravitoelectromagnetism and gravity with torsion, are areas of active research from the theoretical side but it’s the author’s conviction that these studies will eventually reveal many astonishing practical (technological) applications. Main motivations and research lines: - To deepen the study on the profound relation between geometry and physics and the nature of space and time; - To study the analogies and physical coupling between gravity and electromagnetism using geometrical methods, considering the possibility of important theoretical (and technological) applications, being relevant for astrophysics, cosmology and, eventually, for the search of a consistent theory of quantum gravity; - To study gravitoelectromagnetism from a theoretical point of view as well as its astrophysical and technological applications; - To explore the notion of torsion in differential geometry and its importance in physics, namely in classical and quantum gravitation, unified theories of interactions and cosmology; - To explore, using the already mentioned analogies, to which extent is it possible to have a geometrical explanation of “inertial forces” (compatible with the equivalence principle), seen as geometrical deformations of space-time, such as curvature and torsion. (Not all of these topics are covered in the present work but these are the main research lines that motivate this and future projects) General conceptual framework and main topics present in this thesis Relation between geometry and physics: Importance of geometrical methods in the study of the electromagnetic and gravitational fields and in the exploration of the analogies and coupling between these physical interactions: - Axiomatic of the electromagnetism; - Coupling between gravity and electromagnetism; - Gravitoelectromagnetism and GP-B experiment; - Gravity with torsion: • Theoretical relevance of extended theories of gravity. Different models with torsion and interpretations; • Some cosmological applications; • Exploration of the analogies and coupling between gravity and electromagnetism. • Testing space-time torsion - The work suggests the idea that the electromagnetic properties of “empty space” might be interpreted as geometrical properties of the space-time continuum and that electromagnetic and gravitational waves should be fundamentally connected and be mutually generated. In this sense, it also reinforces the need to rethink the concept of “vacuum” in physics. It is also briefly explored the possibility of a geometrical description of the electromagnetic field.. - Being essentially devoted to geometrical methods in the study of the electromagnetic and gravitational fields and to the role of space-time (geometrical) structures in these field theories, this work enhances the philosophical debate on the nature of space and time inspired by ideas coming from physics. On the last part it discusses some relevant open questions such as the possibility of a coherent physicalism of space-time and the geometrization of fundamental structures such as Higgs fields