764 research outputs found
Class of colliding plane waves in terms of Jacobi functions
We present a general class of noncolinear colliding wave solutions of the
Einstein-Maxwell equations given in terms of fourth order polynomials, which in
turn can be expressed through Jacobi functions depending on generalized
advanced and retarded time coordinates. The solutions are characterized by six
free parameters. The parameters can be chosen in such a way to avoid the
generic focusing singularityComment: 25 pages, Latex, uses revtex macro
A set of basis functions to improve numerical calculation of Mie scattering in the Chandrasekhar-Sekera representation
Numerical calculations of light propagation in random media demand the
multiply scattered Stokes intensities to be written in a common fixed
reference. A particularly useful way to perform automatically these basis
transformations is to write the scattered intensities in the
Chandrasekhar-Sekera representation. This representation produces side effects
so that numerical tests are necessary to deal with the limiting situations of
the small-particle (Rayleigh) and forward/backward scattering. Here a new set
of basis functions is presented to describe the scattering of light by
spherical particles (Mie scattering) in the Chandrasekhar-Sekera
representation. These basis functions can be implemented in a new algorithm to
calculate the Mie scattering amplitudes, which leads straightforwardly to all
the scattering quantities. In contrast to the traditional implementation, this
set of basis functions implies to natural numerical convergence to the above
mentioned limiting cases, which are thoroughly discussed.Comment: 8 pages and 2 figure
Chandrasekhar polynomials - A brief review (Analysis of inverse problems through partial differential equations and related topics)
A review on the Chandrasekhar polynomials is given. The polynomials often appear in transport theory. The relation to the method of rotated reference frames for the three-dimensional radiative transport equation is clarified
Chandrasekhar theory of electromagnetic scattering from strongly conducting ellipsoidal targets
Exactly soluble models in the theory of electromagnetic propagation and
scattering are essentially restricted to horizontally stratified or spherically
symmetric geometries, with results also available for certain waveguide
geometries. However, there are a number of new problems in remote sensing and
classification of buried compact metallic targets that require a wider class of
solutions that, if not exact, at least support rapid numerical evaluation.
Here, the exact Chandrasekhar theory of the electrostatics of heterogeneously
charged \emph{ellipsoids} is used to develop a "mean field" perturbation theory
of low frequency electrodynamics of highly conducting ellipsoidal targets, in
insulating or weakly conducting backgrounds. The theory is based formally on an
expansion in the parameter , where is the
characteristic linear size of the scatterer and is the
electromagnetic skin depth. The theory is then extended to a numerically
efficient description of the intermediate-to-late-time dynamics following an
excitation pulse. As verified via comparisons with experimental data taken
using artificial spheroidal targets, when combined with a previously developed
theory of the high frequency, early-time regime, these results serve to cover
the entire dynamic range encountered in typical measurements.Comment: 36 pages, 10 figure
Nonminimal derivative coupling scalar-tensor theories: odd-parity perturbations and black hole stability
We derive the odd parity perturbation equation in scalar-tensor theories with
a non minimal kinetic coupling sector of the general Horndeski theory, where
the kinetic term is coupled to the metric and the Einstein tensor. We derive
the potential of the perturbation, by identifying a master function and
switching to tortoise coordinates. We then prove the mode stability under
linear odd- parity perturbations of hairy black holes in this sector of
Horndeski theory, when a cosmological constant term in the action is included.
Finally, we comment on the existence of slowly rotating black hole solutions in
this setup and discuss their implications on the physics of compact objects
configurations, such as neutron stars.Comment: Important references adde
Historical and other Remarks on Hidden Symmetries
Apart from a few remarks on lattice systems with global or gauge symmetries,
most of this talk is devoted to some interesting ancient examples of symmetries
and their breakdowns in elasticity theory and hydrodynamics. Since Galois
Theory is in many ways the origin of group theory as a tool to analyse (hidden)
symmetries, a brief review of this profound mathematical theory is also given.Comment: 20 pages, 6 postscript figures included, uses AMS-Te
Fermions in the Rindler spacetime
In this paper we study the Dirac equation in the Rindler spacetime. The
solution of the wave equation in an accelerated reference frame is obtained.
The differential equation associated to this wave equation is mapped into a
Sturm-Liouville problem of a Schr\"odinger-like equation. We derive a compact
expression for the energy spectrum associated with the Dirac equation in an
accelerated reference. It is shown that the noninertial effect of the
accelerated reference frame mimics an external potential in the Dirac equation
and, moreover, allows the formation of bound states
The massive Dirac field on a rotating black hole spacetime: Angular solutions
The massive Dirac equation on a Kerr-Newman background may be solved by the
method of separation of variables. The radial and angular equations are coupled
via an angular eigenvalue, which is determined from the Chandrasekhar-Page (CP)
equation. Obtaining accurate angular eigenvalues is a key step in studying
scattering, absorption and emission of the fermionic field.
Here we introduce a new method for finding solutions of the CP equation.
First, we introduce a novel representation for the spin-half spherical
harmonics. Next, we decompose the angular solutions of the CP equation (the
mass-dependent spin-half spheroidal harmonics) in the spherical basis. The
method yields a three-term recurrence relation which may be solved numerically
via continued-fraction methods, or perturbatively to obtain a series expansion
for the eigenvalues. In the case (where and
are the frequency and mass of the fermion) we obtain eigenvalues and
eigenfunctions in closed form. We study the eigenvalue spectrum, and the zeros
of the maximally co-rotating mode.
We compare our results with previous studies, and uncover and correct some
errors in the literature. We provide series expansions, tables of eigenvalues
and numerical fits across a wide parameter range, and present plots of a
selection of eigenfunctions. It is hoped this study will be a useful resource
for all researchers interested in the Dirac equation on a rotating black hole
background.Comment: 22 pages, 6 figures. Minor corrections, to match published versio
Solution of the Dirac equation in the rotating Bertotti-Robinson spacetime
The Dirac equation is solved in the rotating Bertotti-Robinson spacetime. The
set of equations representing the Dirac equation in the Newman-Penrose
formalism is decoupled into an axial and angular part. The axial equation,
which is independent of mass, is solved exactly in terms of hypergeometric
functions. The angular equation is considered both for massless (neutrino) and
massive spin-(1/2) particles. For the neutrinos, it is shown that the angular
equation admits an exact solution in terms of the confluent Heun equation. In
the existence of mass, the angular equation does not allow an analytical
solution, however, it is expressible as a set of first order differential
equations apt for numerical study.Comment: 17 pages, no figure. Appeared in JMP (May, 2008
Stochastic Methods and Dynamical Wave-function Collapse
This brief article reviews stochastic processes as relevant to dynamical
models of wave-function collapse, and is supplemental material for the review
article arXiv:1204.4325Comment: 17 pages, supplemental material to arXiv:1204.4325 [quant-ph],
separated from original review article to meet Rev. Mod. Phys. page limit
requiremen
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