190 research outputs found
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
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
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
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
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
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
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
- …