2,989 research outputs found
Decay of the Maxwell field on the Schwarzschild manifold
We study solutions of the decoupled Maxwell equations in the exterior region
of a Schwarzschild black hole. In stationary regions, where the Schwarzschild
coordinate ranges over , we obtain a decay rate of
for all components of the Maxwell field. We use vector field methods
and do not require a spherical harmonic decomposition.
In outgoing regions, where the Regge-Wheeler tortoise coordinate is large,
, we obtain decay for the null components with rates of
, , and . Along the event horizon and in ingoing regions, where ,
and when , all components (normalized with respect to an ingoing null
basis) decay at a rate of C \uout^{-1} with \uout=t+r_* in the exterior
region.Comment: 37 pages, 5 figure
On the electromagnetic scattering from infinite rectangular conducting grids
The study and development of two numerical techniques for the analysis of electromagnetic scattering from a rectangular wire mesh are described. Both techniques follow from one basic formulation and they are both solved in the spectral domain. These techniques were developed as a result of an investigation towards more efficient numerical computation for mesh scattering. These techniques are efficient for the following reasons: (a1) make use of the Fast Fourier Transform; (b2) they avoid any convolution problems by converting integrodifferential equations into algebraic equations; and (c3) they do not require inversions of any matrices. The first method, the SIT or Spectral Iteration Technique, is applied for regions where the spacing between wires is not less than two wavelengths. The second method, the SDCG or Spectral Domain Conjugate Gradient approach, can be used for any spacing between adjacent wires. A study of electromagnetic wave properties, such as reflection coefficient, induced currents and aperture fields, as functions of frequency, angle of incidence, polarization and thickness of wires is presented. Examples and comparisons or results with other methods are also included to support the validity of the new algorithms
Computer prediction of dual reflector antenna radiation properties
A program for calculating radiation patterns for reflector antennas with either smooth analytic surfaces or with surfaces composed of a number of panels. Techniques based on the geometrical optics (GO) approach were used in tracing rays over the following regions: from a feed antenna to the first reflector surface (subreflector); from this reflector to a larger reflector surface (main reflector); and from the main reflector to a mathematical plane (aperture plane) in front of the main reflector. The equations of GO were also used to calculate the reflected field components for each ray making use of the feed radiation pattern and the parameters defining the surfaces of the two reflectors. These resulting fields form an aperture distribution which is integrated numerically to compute the radiation pattern for a specified set of angles
Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
We give a model of the higher-dimensional spherically symmetric gravitational
collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation
of the basic equations is given for the spacetime with a perfect fluid and a cosmological constant. This is a
generalization of the Misner-Sharp formalism of the four-dimensional
spherically symmetric spacetime with a perfect fluid in general relativity. The
whole picture and the final fate of the gravitational collapse of a dust cloud
differ greatly between the cases with and . There are two
families of solutions, which we call plus-branch and the minus-branch
solutions. Bounce inevitably occurs in the plus-branch solution for ,
and consequently singularities cannot be formed. Since there is no trapped
surface in the plus-branch solution, the singularity formed in the case of
must be naked. In the minus-branch solution, naked singularities are
massless for , while massive naked singularities are possible for
. In the homogeneous collapse represented by the flat
Friedmann-Robertson-Walker solution, the singularity formed is spacelike for , while it is ingoing-null for . In the inhomogeneous collapse with
smooth initial data, the strong cosmic censorship hypothesis holds for and for depending on the parameters in the initial data, while a
naked singularity is always formed for . These naked
singularities can be globally naked when the initial surface radius of the dust
cloud is fine-tuned, and then the weak cosmic censorship hypothesis is
violated.Comment: 23 pages, 1 figure, final version to appear in Physical Review
Coarse Brownian Dynamics for Nematic Liquid Crystals: Bifurcation Diagrams via Stochastic Simulation
We demonstrate how time-integration of stochastic differential equations
(i.e. Brownian dynamics simulations) can be combined with continuum numerical
bifurcation analysis techniques to analyze the dynamics of liquid crystalline
polymers (LCPs). Sidestepping the necessity of obtaining explicit closures, the
approach analyzes the (unavailable in closed form) coarse macroscopic
equations, estimating the necessary quantities through appropriately
initialized, short bursts of Brownian dynamics simulation. Through this
approach, both stable and unstable branches of the equilibrium bifurcation
diagram are obtained for the Doi model of LCPs and their coarse stability is
estimated. Additional macroscopic computational tasks enabled through this
approach, such as coarse projective integration and coarse stabilizing
controller design, are also demonstrated
How to detect an anti-spacetime
Is it possible, in principle, to measure the sign of the Lapse? We show that
fermion dynamics distinguishes spacetimes having the same metric but different
tetrads, for instance a Lapse with opposite sign. This sign might be a physical
quantity not captured by the metric. We discuss its possible role in quantum
gravity.Comment: Article awarded with an "Honorable Mention" from the 2012 Gravity
Foundation Award. 6 pages, 8 (pretty) figure
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