arXiv subjects

Francisco Cabral

Publications and source records attributed to Francisco Cabral.

10 recordsLinked to original sources

arXiv2021

Imprints from a Riemann-Cartan space-time on the energy levels of Dirac spinors

In this work, we investigate the effects of the torsion-fermionic interaction on the energy levels of fermions within a Riemann-Cartan geometry using a model-independent approach. We consider the case of fermions minimally coupled to the background torsion as well as non-minimal extensions via additional couplings with the vector and axial fermionic currents which include parity-breaking interactions. In the limit of zero-curvature, and for the cases of constant and spherically symmetric torsion, we find a Zeeman-like effect on the energy levels of fermions and anti-fermions depending on whether they are aligned/anti-aligned with respect to the axial vector part of the torsion (or to specific combination of torsion quantities), and determine the corresponding fine-structure energy transitions. We also discuss non-minimal couplings between fermionic fields and torsion within the Einstein-Cartan theory and its extension to include the (parity-breaking) Holst term. Finally we elaborate on the detection of torsion effects related to the splitting of energy levels in astrophysics, cosmology and solid state physics using current capabilities.

gr-qc↗

arXiv2020

Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity: Prospects for Unified Field Theories

Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gauge theories of gravity, their field equations and Noether conserved currents, which are the sources of gravity. We then discuss several topics of the gauge approach to gravitational phenomena, namely, quadratic Poincaré gauge models, the~Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of general relativity, quadratic metric-affine Lagrangians, non-Lorentzian connections, and the breaking of Lorentz invariance in the presence of non-metricity. We also highlight the probing of post-Riemannian geometries with test matter. Finally, we briefly discuss some perspectives regarding the role of both geometrical methods and symmetry principles towards unified field theories and a new spacetime paradigm, motivated from the gauge approach to gravity.

gr-qc↗

arXiv2020

The cosmological principle in theories with torsion: The case of Einstein-Cartan-Dirac-Maxwell gravity

We address the implementation of the cosmological principle, that is, the assumption of homogeneity and isotropy in the spatial distribution of matter in the Universe, within the context of Einstein-Cartan theory including minimal couplings of both Dirac and Maxwell fields to torsion. This theory gives rise to new physical effects in environments of high spin densities while leaving the vacuum dynamics unaffected. Our approach is to impose the cosmological principle from the onset to the geometrical degrees of freedom (metric and torsion functions), which constrains the torsion components and the corresponding correction terms in the Friedmann-like equations and in the resulting fermionic and bosonic (non-linear) dynamics. We derive the corresponding cosmological dynamics for the geometrical and matter degrees of freedom and discuss the validity of this approach.

gr-qc↗

arXiv2020

Cosmological bounces, cyclic universes, and effective cosmological constant in Einstein-Cartan-Dirac-Maxwell theory

Einstein-Cartan theory is an extension of the standard formulation of General Relativity characterized by a non-vanishing torsion. The latter is sourced by the matter fields via the spin tensor, and its effects are expected to be important at very high spin densities. In this work we analyze in detail the physics of Einstein-Cartan theory with Dirac and Maxwell fields minimally coupled to the spacetime torsion. This breaks the $U(1)$ gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe. The resulting Dirac-like and Maxwell-like equations are non-linear with self-interactions as well as having fermion-boson non-minimal couplings. We discuss several cosmological aspects of this theory, including bounces, acceleration phases and matter-antimatter asymmetry in the torsion era, as well as late-time effects such as the generation of an effective cosmological constant, dark energy, and future bounces within cyclic solutions.

gr-qc↗

arXiv2019

Einstein-Cartan-Dirac gravity with $U(1)$ symmetry breaking

Einstein-Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities. In this work we introduce an extension of the Einstein-Cartan-Dirac theory with an electromagnetic (Maxwell) contribution minimally coupled to torsion. This contribution breaks the $U(1)$ gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe, yielding new physics in extreme (spin) density regimes. We obtain the generalized gravitational, electromagnetic and fermionic field equations for this theory, estimate the strength of the corrections, and discuss the corresponding phenomenology. In particular, we briefly address some astrophysical considerations regarding the relevance of the effects which might take place inside ultra-dense neutron stars with strong magnetic fields (magnetars).

gr-qc↗

arXiv2017

Electrodynamics and spacetime geometry: Astrophysical applications

After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Ampère laws where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena such as: the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.

gr-qc↗

arXiv2017

Gravitational waves and electrodynamics: New perspectives

Given the recent direct measurement of gravitational waves (GWs) by the LIGO-VIRGO collab- oration, the coupling between electromagnetic fields and gravity have a special relevance since it opens new perspectives for future GW detectors and also potentially provides information on the physics of highly energetic GW sources. We explore such couplings using the field equations of electrodynamics on (pseudo) Riemann manifolds and apply it to the background of a GW, seen as a linear perturbation of Minkowski geometry. Electric and magnetic oscillations are induced that propagate as electromagnetic waves and contain information about the GW which generates them. The most relevant results are the presence of longitudinal modes and dynamical polarization patterns of electromagnetic radiation induced by GWs. These effects might be amplified using appropriate resonators, effectively improving the signal to noise ratio around a specific frequency. We also briefly address the generation of charge density fluctuations induced by GWs and the implications for astrophysics.

gr-qc↗

arXiv2016

Electrodynamics and spacetime geometry I: Foundations

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We briefly review the foundations of electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations which introduce the spacetime metric. We then proceed with the tensor formulation by assuming local, linear, homogeneous and isotropic constitutive relations, and explore the physical, observable consequences of Maxwell's equations in curved spacetime. The field equations, charge conservation and the Lorentz force are explicitly expressed in general (pseudo) Riemanian manifolds. The generalized Gauss and Maxwell-Ampère laws, as well as the wave equations, reveal potentially interesting astrophysical applications. In all cases new electromagnetic couplings and related phenomena are induced by spacetime curvature. The implications and possible applications for gravity waves detection are briefly addressed. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

gr-qc↗

arXiv2015

The quantum realm of the "Little Sibling" of the Big Rip singularity

We analyse the quantum behaviour of the "Little Sibling" of the Big Rip singularity (LSBR) [1]. The quantisation is carried within the geometrodynamical approach given by the Wheeler--DeWitt (WDW) equation. The classical model is based on a Friedmann--Lemaître--Robertson--Walker Universe filled by a perfect fluid that can be mapped to a scalar field with phantom character. We analyse the WDW equation in two setups. In the first step, we consider the scale factor as the single degree of freedom, which from a classical perspective parametrises both the geometry and the matter content given by the perfect fluid. We then solve the WDW equation within a WKB approximation, for two factor ordering choices. On the second approach, we consider the WDW equation with two degrees of freedom: the scale factor and a scalar field. We solve the WDW equation, with the Laplace--Beltrami factor-ordering, using a Born--Oppenheimer approximation. In both approaches, we impose the DeWitt (DW) condition as a potential criterion for singularity avoidance. We conclude that in all the cases analysed the DW condition can be verified, which might be an indication that the LSBR can be avoided or smoothed in the quantum approach.

gr-qc↗

arXiv2014

Short note on the Sirenia disappearance from the Euro-North African realm during the Cenozoic: a link between climate and Supernovae?

Sirenia are marine mammals that colonized the European shores up to 2.7 Ma. Their biodiversity evolution follows the climate evolution of the Cenozoic. However, several climate events, as well as the global climate trend of this Era are still struggling to be understood. When considering only Earth processes, the climate evolution of the Cenozoic is hard to understand. If the galactic environment is taken into account, some of these climate events, as well as the global climate trend, became more easily understood. The Milky Way, through Supernovae, may bring some answers to why Cenozoic climate had this evolution. With the assumption that SN can induced changes in Earth climate in long time scales, Sirenia disappearance from Europe would be a side effect of this process.

q-bio.PE↗