arXiv subjects
Publications and source records attributed to E. Bittencourt.
We analyze the recently obtained static and spherically symmetric solution of the Spinor Theory of Gravity (STG) which, in the weak field limit, presents an effective Newtonian potential that contains an extra logarithmic behavior. We apply this solution to the description of the galaxy rotation curves finding an interesting analogy with the dark matter halo profile proposed by Navarro, Frenk and White.
Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein's field equations where the spatial sections are flat and the source is a non-perfect fluid such that the dissipative terms can be written in terms of spatial gradients of the energy density under a suitable choice of the coordinate system. It is shown through the calculation of the luminosity distance as a function of the redshift that the presence of such inhomogeneities may lead to an effective deceleration parameter compatible with either the standard $Λ$CDM model or LTB models depending on the choice of boundary conditions with no exotic matter. This fact is another evidence that different inhomogeneous models should be carefully investigated in order to verify which model may be compatible with observations and still be as close as possible to the standard model regarding the underlying assumptions, without resorting necessarily to exotic matter components.
Hadamard-Papapetrou method of field discontinuities is here employed in order to determine the effective metric that describes the propagation of acoustic perturbations in isentropic fluids. It is shown that, when dissipative effects are present, small perturbations in fastly moving fluids have a natural description in terms of an effective acoustic geometry. As an application of our results, a model for an acoustic black hole in viscous fluid is investigated.
Crude comparison between four alternative proposals for the very definition of a wormhole is provided, all of which were intended to apply to the dynamical cases. An interesting dynamical solution, based upon large scale magnetic fields, is used for the comparisons. Such solution goes beyond the perfect fluid approximation due to an anisotropic pressure component, bringing to the fore some unsuspected features of those definitions. Certain notions as reversible traversability are claimed as a way to select among those definitions the best suited one to represent our intuition of what a wormhole solution is expected to be.
We discuss a class of models for gravity based on a scalar field. The models include and generalize the old approach by Nordström which predated and in some way inspired General Relativity. The class include also a model that we have recently introduced and discussed in its cosmological aspects (GSG). We present here a complete characterisation of the Schwarschild geometry as a vacuum solution of GSG and sketch a discussion of the first Post-Newtonian approximation.
We describe what cosmology looks like in the context of the geometric theory of gravity (GSG) based on a single scalar field. There are two distinct classes of cosmological solutions. An interesting feature is the possibility of having a bounce without invoking exotic equations of state for the cosmic fluid. We also discuss cosmological perturbation and present the basis of structure formation by gravitational instability in the framework of the geometric scalar gravity.
Propagation of light in nonlinear materials is here studied in the regime of the geometrical optics. It is shown that a spherically symmetric medium at rest with some specific dielectric properties can be used to produce an exact analogue model for a class of space-times which includes spherically symmetric and static black hole solutions. The optical model here presented can be a useful tool to reproduce in laboratory the behavior of optical null geodesics near a compact object with an observable gravitational Schwarzschild radius.
We present the expression $t_{μν}$ of the energy-momentum tensor of the gravitational field in the framework of the recent proposal of the Geometric Scalar theory of gravity (GSG). From the conservation of $t_{μν}$ it follows the dynamics of the gravitational field. As an example of this expression for $t_{μν}$ we calculate the gravitational energy of a compact object.
We investigate a new form of contribution for the anomalous magnetic moment of all particles. This common origin is displayed in the framework of a recent treatment of electrodynamics that is based in the introduction of an electromagnetic metric which has no gravitational character. This effective metric constitutes a universal pure electromagnetic process perceived by all bodies, charged or not charged. As a consequence it yields a complementary explanation for the existence of anomalous magnetic moment for charged particles and even for non-charged particles like neutrino.
We have solved the Einstein equations of general relativity for a class of metrics with constant spatial curvature and found a non-vanishing Weyl tensor in the presence of an energy-momentum tensor with an anisotropic pressure component. The time evolution of the spacetime is guided by the usual Friedmann equations and the constraints on the hypersurface comprise a separated system of equations that can be independently solved. Contrary to the apparent behavior induced by some choices of coordinates, the metric we have obtained is completely regular everywhere and is free of singularities (except the well-known Friedmann singularity at $t=0$). The physical features of this solution are elucidated by using the Quasi-Maxwellian equations (a set of third order differential equations describing the dynamics of the gravitational field in terms of the Weyl tensor). The motion of test particles is also analyzed in order to confirm the maximal extension of the manifold under consideration. These results indicate that the anisotropic pressure could mimic dark matter effects on certain geodesic congruences keeping the cosmic flow unchanged.
A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent quantities. We shall see that in the QM-scheme we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz et al that deals with perturbation in the standard Einstein framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting on particular choices of the perturbed variables as a combination of gauge dependent quantities.
We present a geometric scalar theory of gravity. Our proposal will be described using the "background field method" introduced by Gupta, Feynman and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor - which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models - does not apply to our geometric scalar theory. Some consequences of the new scalar theory are explored.
We show that Gordon metric belongs to a larger class of geometries, which are responsible to describe the paths of accelerated bodies in moving dielectrics as geodesics in a metric $\hat q_{μν}$ different from the background one. This map depends only on the background metric and on the motion of the bodies under consideration. As a consequence, this method describes a more general property that concerns the elimination of any kind of force acting on bodies by a suitable change of the substratum metric.
The purpose of this paper is to present a unified description of mass generation mechanisms that have been investigated so far and that are called the Mach and Higgs proposals. In our mechanism, gravity acts merely as a catalyst and the final expression of the mass depends neither on the intensity nor on the particular properties of the gravitational field. We shall see that these two strategies to provide mass for all bodies that operate independently and competitively can be combined into a single unified theoretical framework. As a consequence of this new formulation we are able to present an answer to the question: what is the origin of the mass of the Higgs boson?
We show that the path of any accelerated body in an arbitrary space-time geometry $g_{μν}$ can be described as geodesics in a dragged metric $\hat{q}_{μν}$ that depends only on the background metric and on the motion of the body. Such procedure allows the interpretation of all kind of non-gravitational forces as modifications of the metric of space-time. This method of effective elimination of the forces by a change of the metric of the substratum can be understood as a generalization of the d'Alembert principle applied to all relativistic processes.
With the eminent confirmation or disproof of the existence of Higgs boson by experiments on the LHC it is time to analyze in a non-dogmatic way the suggestions to understand the origin of the mass. Here we analyze the recent proposal according to which gravity is what is really responsible for the generation of mass of all bodies. The great novelty of such mechanism is that the gravitational field acts merely as a catalyst, once the final expression of the mass does not depend either on the intensity or on the particular characteristics of the gravitational field.
We present the whole class of Gaussian coordinate systems for the Kerr metric. This is achieved through the uses of the relationship between Gaussian observers and the relativistic Hamilton-Jacobi equation. We analyze the completeness of this coordinate system. In the appendix we present the equivalent JEK formulation of General Relativity -- the so-called quasi-Maxwellian equations -- which acquires a simpler form in the Gaussian coordinate system. We show how this set of equations can be used to obtain the internal metric of the Schwazschild solution, as a simple example. We suggest that this path can be followed to the search of the internal Kerr metric.