We show that nonlinear dynamics of a scalar field ϕ may be described as a modification of the spacetime geometry. Thus, the self-interaction is interpreted as a coupling of the scalar field with an effective gravitational metric that is constructed with ϕ itself.We prove that this process is universal, that is, it is valid for an arbitrary Lagrangian. Our […]

## The gravitational mechanism to generate mass

The purpose of this work is to show that the gravitational interaction is able to generate mass for all bodies. The condition for this is the existence of an energy distribution represented by the vacuum or the cosmological constant. Author: M. Novello. Artigo em PDF

## Geometric scalar theory of gravity

We present a geometric scalar theory of gravity. Our proposal will be described using the “background field method” introduced by Gupta, Feynman, Deser 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 […]

## Geometrizing Relativistic Quantum Mechanics

We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version […]

## Eletromagnectic Geometry

We show that Maxwell’s electromagnetism can be mapped into the Born-Infeld theory in a curved space-time which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants F and G confirming that we have included all possible solutions of Maxwell’s equations. Our result seems to show […]

## On a geometrical description of quantum mechanics

We show that quantum mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular affine space, which we call Q-wis. This is proved using the Bohm–de Broglie causal formulation of quantum mechanics. In the Q-wis geometry, the length of extended objects changes from point to point. In this […]

## Gaussian Coordinate Systems for the Kerr Metric

We present a class of Gaussian coordinate systems for the Kerr metric obtained from the relativistic Hamilton-Jacobi equation. We discuss the Cauchy problem of such a coordinate system. In the appendix, we present the JEK (Jordan-Ehlers-Kundt) formulation of General Relativity—the so-called quasi-Maxwell equations—which acquires a simpler form in the Gaussian coordinate system. We show how […]

## Toy model of a fake inflation

Discontinuities in nonlinear field theories propagate through null geodesics in an effective metric that depends on its dynamics and on the background geometry. Once information of the geometry of the universe comes mostly from photons, one should carefully analyze the effects of possible nonlinearities on electrodynamics in the cosmic geometry. Such a phenomenon of induced […]

## Extended Born-Infeld dynamics and cosmology

We introduce an extension of the Born-Infeld action for a scalar field and show that it can act as unifying dark matter, providing an explanation for both structure formation and the accelerated expansion of the universe. We investigate the cosmological dynamics of this theory in a particular case, referred to as the ‘‘Milne-Born-Infeld’’ (MBI) Lagrangian. […]

## Effective geometry in nonlinear electrodynamics

The electromagnetic force a photon undergoes in a nonlinear regime can be geometrized. This is a rather unexpected result and at the same time a beautiful consequence of the analysis of the behavior of the discontinuities of non-homogeneous nonlinear electromag- netic field. We show how such geometrization is possible. Artigo em PDF

## Effective electromagnetic geometry

We show that the propagation of photons in a nonlinear dielectric medium can be described in terms of a modification of the metric structure of space-time. We solve completely the case in which the dielectric constant is an arbitrary function of the electric field (E). The particular case of no dependence on the field reduces […]

## Constructing Dirac linear fermions in terms of non-linear Heisenberg spinors

We show that the massive (or massless) neutrinos can be described as special states of Heisenberg nonlinear spinors. As a by-product of this decomposition a particularly attractive consequence appears: the possibility of relating the existence of only three species of mass-less neutrinos to such internal non-linear structure. At the same time it allows the possibility […]

## Cosmology in geometric scalar gravity

We describe what cosmology looks like in the context of the geometric theory of gravity 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 […]

## The cosmological origin of the Nambu Jona-Lasinio model

Recently a mechanism to generate mass from gravitational interaction, based on Mach principle, according to which the inertia of a body is a property of matter as well as of the background provided by the rest-of-the-universe was presented in Refs. 1, 2. In these papers such an idea was realized for scalar and spinor fields […]

## Repulsive gravity generated by ordinary matter

In the present work, and idea first discussed in the early 80’s is rediscussed. The model consists of a scalar field non-minimally coupled to gravity with a quartic self-interaction potential. After a spontaneous symmetry braking process, the scalar field promotes a renormalization of the gravitational constant, which in certain regimes can lead to gravitational repulsive effects produced […]

## Cosmic spinning string and causal protecting capsules

A method by which a geometry with causality violation can be taken as a part of a globally causal space-time model is presented. This procedure is applied to a pair of extensions to Godel s space-time: a “Godel-generalized” and a stringlike solution. The latter is shown to be an intermediate region between Godel and deformed […]

## Metric Relativity and the Dynamical Bridge: Highlights of Riemannian Geometry in Physics

We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research: the Metric Relativity and the Dynamical Bridge. We describe the notion of equivalent (dragged) metric gμν which is responsible to map […]

## Extended Born-Infeld theory and the bouncing magnetic universe

We show that a generalized Born-Infeld electrodynamics responsible for regular configurations of the static field of a charged particle produces a nonsingular universe that contains a bouncing. This means that the Universe has a previous collapsing phase, attains a minimum value for its scale factor and then enters into an expanding phase. We exhibit such […]

## Bouncing cosmologies

We review the general features of nonsingular universes (i.e. those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also […]

## Beyond analog gravity: the case of exceptional dynamics

We show that it is possible to go beyond the propagation aspects usually contemplated in the analog models of gravity. Until now, the emergence of a metric appears in the description of excitations around a given background solution or in the study of field discontinuities in the geometrical optics regime. We now overcome some limitations […]

## A proposal for the origin of the anomalous magnetic moment

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 on the introduction of an electromagnetic metric which has no gravitational character. This effective metric constitutes a universal pure electro- magnetic process perceived […]

## Analogue black holes for light rays in static dielectrics

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 sym- metric and static black hole solutions. […]

## A massa do neutrino

Preconceito teórico dificultou durante décadas avanço na compreensão de partícula. O Nobel de Física deste ano foi dado a dois cientistas que mos- traram que os neutrinos, partículas extremamente evasivas e mui- to abundantes no Universo, possuem massa. Até muito recente- mente acreditava-se que elas viajavam com a velocidade da luz, isto é, que sua […]

## Metric Relativity and the Dynamical Bridge: highlights of Riemannian geometry in physics

We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research: the Metric Relativity and the Dynamical Bridge. We describe the notion of equivalent (dragged) metric gμν which is responsible to map […]

## Closed Lightlike Curves in Non-linear Electrodynamics

We show that non-linear electrodynamics may induce a photon to follow a closed path in spacetime. We exhibit a specific case in which such closed lightlike curve (CLC) appears. M. Novello, V. A. De Lorenci, E. Elbaz and J. M. Salim Artigo em PDF

## Singularities in General Relativity coupled to nonlinear electrodynamics

We study here some consequences of the nonlinearities of the electromagnetic field acting as a source of Einstein’s equations on the propagation of photons. We restrict to the particular case of a “regular black hole”, and show that there exist singularities in the effective geometry. These singularities may be hidden behind a horizon or naked, […]

## Extended Born-Infeld theory and the bouncing magnetic universe

We show that a generalized Born-Infeld Electrodynamics responsible for regular configurations of the static field of a charged particle produces a non-singular universe that contains a bouncing. This means that the universe has a previous collapsing phase, attains a minimum value for its scale factor and then enters into an expanding phase. We exhibit such […]

## What is the origin of the mass of the Higgs bóson?

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 […]

## Gordon metric revisited

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 $\hat q_{\mu\nu}$ different from the background one. This map depends only on the background metric and on the motion of the bodies under consideration. Novello […]

## Dragged metrics

We show that the path of any accelerated body in an arbitrary space-time geometry $ g_{\mu\nu} $ can be described as geodesics in a dragged metric $ \hat{q}_{\mu\nu} $ 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 […]

## The quasi-Maxwellian equations of general relativity: applications to the perturbation theory

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-Lemaitre-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent […]

## Analogue black holes for light rays in static dielectrics

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 […]

## Chiral symmetry breaking as a geometrical process

This paper is an extension for spinor fields of the recently developed Dynamical Bridge formalism which relates a linear dynamics in a curved space to a nonlinear dynamics in Minkowski space. This leads to a new geometrical mechanism to generate a chiral symmetry breaking without mass, providing an alternative explanation for the absence of right-handed […]