Electrodynamics and Spacetime Geometry: 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 review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. 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.     

A Domain of Spacetime Intervals in General Relativity

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emerges from something discrete.     

On the Philosophical Foundations of Measurements in General Relativity

In this paper, first, the question of what a measurement is in General Relativity is tackled; then, some foundational problems it involves are analysed. In particular, by recalling what a measurement is in general, we will try to precisely define what it is in General Relativity. Then, we will analyse, by means of a suitable example, some foundational problems it involves. It will be stressed that such foundational problems do not arise owing to the gauge invariance or the correlation among the measuring observers but owing to the principle of equivalence.     

Geometry of Quark and Strange Quark Matter in Higher Dimensional General Relativity

In this paper we study quark matter and strange quark matter in higher-dimensional spherical symmetric space-times. We analyze strange quark matter for the different equations of state and obtain the space-time geometry of quark and strange quark matter. We also discuss the features of the obtained solutions in the context of higher-dimensional general theory of relativity.     

General Relativity on a Null Surface: Hamiltonian Formulation in the Teleparallel Geometry

The Hamiltonian formulation of generalrelativity on a null surface is established in theteleparallel geometry. No particular conditions on thetetrads are imposed, like the time gauge condition. Bymeans of a 3 + 1 decomposition the resultingHamiltonian arises as a completely constrained system.However, it is structurally different from the standardArnowitt–Deser–Misner (adm) typeformulation. In this geometrical framework the basic fieldquantities are tetrads that transform under the globalSO(3, 1) and the torsion tensor.     

Equivalence Between an Extension of Teleparallelism to a Weyl Geometry and General Relativity

Recently, an extension of teleparallelism to a Weyl geometry which allows us to easily establish conformal invariance and “geometrize” electromagnetism has been presented. In this paper, I extend a result which concerns the existence of the Schwarzschild solution to a particular class of this extension. In addition, I obtain the field equations of some models based on this extension, including the one which is equivalent to Einstein’s field equations with a massless scalar field.