2D Born-Infeld electrostatic fields

The electrostatic configurations of the Born-Infeld field in the 2-dimensional Euclidean plane are obtained by means of a non-analytical complex mapping which captures the structure of equipotential and field lines. The electrostatic field reaches the Born-Infeld limit value when the field lines become tangent to an epicycloid around the origin. The total energy by unit of length remains finite.Comment: 4 pages, 2 figure

From aether theory to Special Relativity

At the end of the 19th century light was regarded as an electromagnetic wave propagating in a material medium called ether. The speed c appearing in Maxwell's wave equations was the speed of light with respect to the ether. Therefore, according to the Galilean addition of velocities, the speed of light in the laboratory would differ from c. The measure of such difference would reveal the motion of the laboratory (the Earth) relative to the ether (a sort of absolute motion). However the Earth's absolute motion was never evidenced. Galileo addition of velocities is based on the assumption that lengths and time intervals are invariant (independent of the state of motion). This way of thinking the spacetime emanates from our daily experience and lies at the heart of Newton's Classical Mechanics. Nevertheless, in 1905 Einstein defied Galileo addition of velocities by postulating that light travels at the same speed c in any inertial frame. In doing so, Einstein extended the principle of relativity to the electromagnetic phenomena described by Maxwell's laws. In Einstein's Special Relativity the ether does not exist and the absolute motion is devoid of meaning. The invariance of the speed of light forced the replacement of Galileo transformations with Lorentz transformations. Thus, relativistic length contractions and time dilations entered our understanding of the spacetime. Newtonian mechanics had to be reformulated, which led to the discovery of the mass-energy equivalence.Comment: 24 pages, 9 figures. To appear in Handbook of Spacetime, edited by A. Ashtekar and V. Petkov, Springer-Verlag Gmb

The equivalence principle and the bending of light

The apparent discrepancy between the bending of light predicted by the equivalence principle and its corresponding value in general relativity is resolved by evaluating the deflection of light with respect to a direction that is parallel transported along the ray trajectory in 3-space. In this way the bending predicted by the equivalence principle is fulfilled in general relativity and other alternative metric theories of gravity.Comment: 7 pages, 1 figure, to be published in American Journal of Physic

Two-dimensional solutions for Born-Infeld fields

The non-linear second order Born-Infeld equation is reduced to a simpler first order complex equation, which can be trivially solved for the coordinates as functions of the field. Each solution is determined by the choice of a holomorphic function subjected to boundary conditions. The explanation of the method is accompanied by applications to Born-Infeld electrostatics, magnetostatics and wave propagation.Comment: 10 pages. Minor changes, enlarged and corrected bibliography, published versio

Testing nonlinear electrodynamics in waveguides: the effect of magnetostatic fields on the transmitted power

In Born-Infeld theory and other nonlinear electrodynamics, the presence of a magnetostatic field modifies the dispersion relation and the energy velocity of waves propagating in a hollow waveguide. As a consequence, the transmitted power along a waveguide suffers slight changes when a magnetostatic field is switched on and off. This tiny effect could be better tested by operating the waveguide at a frequency close to the cutoff frequency.Comment: 5 pages. Version to appear in Journal of Physics

Relational Mechanics as a gauge theory

Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the resulting equations of motion are valid in any frame. The compensating terms provide inertial forces depending on the total momentum P, intrinsic angular momentum J and intrinsic inertia tensor I. Therefore, the privileged frames where Newton's equations are valid (Newtonian frames) are completely determined by the matter distribution of the universe (Machianization). At the Hamiltonian level, the gauge invariance leads to first class constraints that remove those degrees of freedom that make no sense once the absolute space has been eliminated. This reformulation of classical mechanics is entirely relational, since it is a dynamics for the distances between particles. It is also Machian, since the rotation of the rest of the universe produces centrifugal effects. It then provides a new perspective to consider the foundational ideas of general relativity, like Mach's principle and the weak equivalence principle. With regard to the concept of time, the absence of an absolute time is known to be a characteristic of parametrized systems. Furthermore, the scale invariance of those parametrized systems whose potentials are inversely proportional to the squared distances can be also gauged by introducing another compensating term associated with the intrinsic virial G (shape-dynamics).Comment: 15 pages, 1 figure. Main changes in Section III; citations adde

f(R) and f(T) theories of modified gravity

We briefly review f(R) theories, both in the metric and Palatini formulations, their scalar-tensor representations and the chameleon mechanism that could explain the absence of perceptible consequences in the Solar System. We also review f(T) theories, a different approach to modified gravity consisting in a deformation of the teleparallel equivalent of General Relativity. We show some applications to cosmology and cosmic strings. As f(R)'s, f(T) theories are not exempted from additional degrees of freedom; we also discuss this still open issue.Comment: 8 pages, 2 figures. To appear in the Proceedings of the CosmoSul conference (Rio de Janeiro, Brazil, 01-05 August 2011). Added reference

Application of exterior calculus to waveguides

Exterior calculus is a powerful tool to search for solutions to the electromagnetic field equations, whose strength can be better appreciated when applied to work out non-trivial configurations. Here we show how to exploit this machinery to obtain the electromagnetic TM and TE modes in hollow cylindrical waveguides. The proper use of exterior calculus and Lorentz boosts will straightforwardly lead to such solutions and the respective power transmitted along the waveguide.Comment: 10 pages. Typos correcte

Spherically symmetric static spacetimes in vacuum f(T) gravity

We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a BTZ-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).Comment: 8 pages. Some typos corrected and references updated. One additional typo corrected in Eq. (33). Accepted for publication in Physical Review D. Final versio