43,778 research outputs found
The Relativistically Spinning Charged Sphere
When the equatorial spin velocity, , of a charged conducting sphere
approaches , the Lorentz force causes a remarkable rearrangement of the
total charge .
Charge of that sign is confined to a narrow equatorial belt at latitudes while charge of the opposite sign
occupies most of the sphere's surface. The change in field structure is shown
to be a growing contribution of the `magic' electromagnetic field of the
charged Kerr-Newman black hole with Newton's G set to zero. The total charge
within the narrow equatorial belt grows as and tends to
infinity as approaches . The electromagnetic field, Poynting vector,
field angular momentum and field energy are calculated for these
configurations.
Gyromagnetic ratio, g-factor and electromagnetic mass are illustrated in
terms of a 19th Century electron model. Classical models with no spin had the
small classical electron radius a hundredth of the Compton
wavelength, but models with spin take that larger size but are so
relativistically concentrated to the equator that most of their mass is
electromagnetic.
The method of images at inverse points of the sphere is shown to extend to
charges at points with imaginary co-ordinates.Comment: 15 pages, 1figur
Self-Interacting Dark Matter Halos and the Gravothermal Catastrophe
We study the evolution of an isolated, spherical halo of self-interacting
dark matter (SIDM) in the gravothermal fluid formalism. We show that the
thermal relaxation time, , of a SIDM halo with a central density and
velocity dispersion of a typical dwarf galaxy is significantly shorter than its
age. We find a self-similar solution for the evolution of a SIDM halo in the
limit where the mean free path between collisions, , is everywhere
longer than the gravitational scale height, . Typical halos formed in this
long mean free path regime relax to a quasistationary gravothermal density
profile characterized by a nearly homogeneous core and a power-law halo where
. We solve the more general time-dependent problem and
show that the contracting core evolves to sufficiently high density that
inevitably becomes smaller than in the innermost region. The core
undergoes secular collapse to a singular state (the ``gravothermal
catastrophe'') in a time , which is longer than the
Hubble time for a typical dark matter-dominated galaxy core at the present
epoch. Our model calculations are consistent with previous, more detailed,
N-body simulations for SIDM, providing a simple physical interpretation of
their results and extending them to higher spatial resolution and longer
evolution times. At late times, mass loss from the contracting, dense inner
core to the ambient halo is significantly moderated, so that the final mass of
the inner core may be appreciable when it becomes relativistic and radially
unstable to dynamical collapse to a black hole.Comment: ApJ in press (to appear in April), 12 pages. Extremely minor changes
to agree with published versio
Quadrature domains and kernel function zipping
It is proved that quadrature domains are ubiquitous in a very strong sense in
the realm of smoothly bounded multiply connected domains in the plane. In fact,
they are so dense that one might as well assume that any given smooth domain
one is dealing with is a quadrature domain, and this allows access to a host of
strong conditions on the classical kernel functions associated to the domain.
Following this string of ideas leads to the discovery that the Bergman kernel
can be zipped down to a strikingly small data set. It is also proved that the
kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati
Inertial frame rotation induced by rotating gravitational waves
We calculate the rotation of the inertial frames within an almost flat
cylindrical region surrounded by a pulse of non-axially-symmetric gravitational
waves that rotate about the axis of our cylindrical polar coordinates. Our
spacetime has only one Killing vector. It is along the z-axis and hypersurface
orthogonal. We solve the Einstein equations to first order in the wave
amplitude and superpose such linearized solutions to form a wave pulse. We then
solve the relevant Einstein equation to second order in the amplitude to find
the rotation of inertial frames produced by the pulse. The rotation is without
time delay. The influence of gravitational wave angular momentum on the
inertial frame demonstrates that Mach's principle can not be expressed in terms
of the influence of the stress-energy-momentum tensor alone but must involve
also influences of gravitational wave energy and angular momentum.Comment: Scheduled to appear in Class. and Quantum Grav. July 2008, "inertial"
added in titl
Dark Matter Annihilation Signatures from Electroweak Bremsstrahlung
We examine observational signatures of dark matter annihilation in the Milky
Way arising from electroweak bremsstrahlung contributions to the annihilation
cross section. It has been known for some time that photon bremsstrahlung may
significantly boost DM annihilation yields. Recently, we have shown that
electroweak bremsstrahlung of W and Z gauge bosons can be the dominant
annihilation channel in some popular models with helicity-suppressed 2 --> 2
annihilation. W/Z-bremsstrahlung is particularly interesting because the gauge
bosons produced via annihilation subsequently decay to produce large correlated
fluxes of electrons, positrons, neutrinos, hadrons (including antiprotons) and
gamma rays, which are all of importance in indirect dark matter searches. Here
we calculate the spectra of stable annihilation products produced via
gamma/W/Z-bremsstrahlung. After modifying the fluxes to account for the
propagation through the Galaxy, we set upper bounds on the annihilation cross
section via a comparison with observational data. We show that stringent cosmic
ray antiproton limits preclude a sizable dark matter contribution to observed
cosmic ray positron fluxes in the class of models for which the bremsstrahlung
processes dominate.Comment: 11 pages, 6 figures. Updated to match PRD versio
Electromagnetic Magic: The Relativistically Rotating Disk
A closed form analytic solution is found for the electromagnetic field of the
charged uniformly rotating conducting disk for all values of the tip speed
up to . For it becomes the Magic field of the Kerr-Newman black hole
with set to zero.
The field energy, field angular momentum and gyromagnetic ratio are
calculated and compared with those of the electron.
A new mathematical expression that sums products of 3 Legendre functions each
of a different argument, is demonstrated.Comment: 10 pages, one figur
Response to Nauenberg's "Critique of Quantum Enigma: Physics Encounters Consciousness"
Nauenberg's extended critique of Quantum Enigma rests on fundamental
misunderstandings.Comment: To be published in Foundations of Physic
Using a Combination of Micro-Computed Tomography, CAD and 3D Printing Techniques to Reconstruct Incomplete 19th-Century Cantonese Chess Pieces
Electromagnetic Fields in Jets
The magnetic fields and energy flows in an astronomical jet described by our
earlier model are calculated in detail. Though the field distribution varies
with the external pressure function p(z), it depends only weakly on the other
boundary conditions. Individual fieldlines were plotted; the lines become
nearly vertical at the bottom and are twisted at the top. An animation of a
fieldline's motion was made, which shows the line being wound up by the
accretion disc's differential rotation and rising as a result of this. The
distribution of Poynting flux within the jet indicates that much of the energy
flows up the jet from the inside of the accretion disc but a substantial
fraction flows back down to the outside.Comment: 8 pages, 5 figures. Accepted for publication in MNRA
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