77,972 research outputs found
Electrodynamics on Cosmological Scales
Maxwell's equations cannot describe a homogeneous and isotropic universe with
a uniformly distributed net charge, because the electromagnetic field tensor in
such a universe must be vanishing everywhere. For a closed universe with a
nonzero net charge, Maxwell's equations always fail regardless of the spacetime
symmetry and the charge distribution. The two paradoxes indicate that Maxwell's
equations need be modified to be applicable to the universe as a whole. We
consider two types of modified Maxwell equations, both can address the
paradoxes. One is the Proca-type equation which contains a photon mass term.
This type of electromagnetic field equations can naturally arise from
spontaneous symmetry breaking and the Higgs mechanism in quantum field theory,
where photons acquire a mass by eating massless Goldstone bosons. However,
photons loose their mass when symmetry is restored, and the paradoxes reappear.
The other type of modified Maxwell equations, which are more attractive in our
opinions, contain a term with the electromagnetic potential vector coupled to
the spacetime curvature tensor. This type of electromagnetic field equations do
not introduce a new dimensional parameter and return to Maxwell's equations in
a flat or Ricci-flat spacetime. We show that the curvature-coupled term can
naturally arise from the ambiguity in extending Maxwell's equations from a flat
spacetime to a curved spacetime through the minimal substitution rule. Some
consequences of the modified Maxwell equations are investigated. The results
show that for reasonable parameters the modification does not affect existing
experiments and observations. However, the field equations with a
curvature-coupled term can be testable in astrophysical environments where mass
density is high or the gravity of electromagnetic radiation plays a dominant
role in dynamics, e.g., interior of neutron stars and the early universe.Comment: 23 pages, including 1 figure. Version matching publication in GR
Time Machines Constructed from Anti-de Sitter Space
In this paper time machines are constructed from anti-de Sitter space. One is
constructed by identifying points related via boost transformations in the
covering space of anti-de Sitter space and it is shown that this Misner-like
anti-de Sitter space is just the Lorentzian section of the complex space
constructed by Li, Xu, and Liu in 1993. The others are constructed by gluing an
anti-de Sitter space to a de Sitter space, which could describe an anti-de
Sitter phase bubble living in a de Sitter phase universe. Self-consistent vacua
for a massless conformally coupled scalar field are found for these time
machines, whose renormalized stress-energy tensors are finite and solve the
semi-classical Einstein equations. The extensions to electromagnetic fields and
massless neutrinos are discussed. It is argued that, in order to make the
results consistent with Euclidean quantization, a new renormalization procedure
for quantum fields in Misner-type spaces (Misner space, Misner-like de Sitter
space, and Misner-like anti-de Sitter space) is required. Such a
"self-consistent" renormalization procedure is proposed. With this
renormalization procedure, self-consistent vacua exist for massless conformally
coupling scalar fields, electromagnetic fields, and massless neutrinos in these
Misner-type spaces.Comment: 17 pages (revtex), 6 figures (4 postscript, 2 gif
K-theory for ring C*-algebras attached to function fields with only one infinite place
We study the K-theory of ring C*-algebras associated to rings of integers in
global function fields with only one single infinite place. First, we compute
the torsion-free part of the K-groups of these ring C*-algebras. Secondly, we
show that, under a certain primeness condition, the torsion part of K-theory
determines the inertia degrees at infinity of our function fields.Comment: 27 page
Observational Signatures of the Magnetic Connection between a Black Hole and a Disk
In this Letter we use a simple model to demonstrate the observational
signatures of the magnetic connection between a black hole and a disk: (1) With
the magnetic connection more energy is dissipated in and radiated away from
regions close to the center of the disk; (2) The magnetic connection can
produce a very steep emissivity compared to the standard accretion; (3) The
observational spectral signature of the magnetic connection can be robust.
These signatures may be identified with the observations of Chandra and
XMM-Newton. In fact, the steep emissivity index for the Seyfert 1 galaxy
MCG--6-30-15 inferred from the recent XMM-Newton observation is very difficult
to be explained with a standard accretion disk but can be easily explained with
the magnetic connection between a black hole and a disk.Comment: 10 pages, 3 figure
Three-Source Extractors for Polylogarithmic Min-Entropy
We continue the study of constructing explicit extractors for independent
general weak random sources. The ultimate goal is to give a construction that
matches what is given by the probabilistic method --- an extractor for two
independent -bit weak random sources with min-entropy as small as . Previously, the best known result in the two-source case is an
extractor by Bourgain \cite{Bourgain05}, which works for min-entropy ;
and the best known result in the general case is an earlier work of the author
\cite{Li13b}, which gives an extractor for a constant number of independent
sources with min-entropy . However, the constant in the
construction of \cite{Li13b} depends on the hidden constant in the best known
seeded extractor, and can be large; moreover the error in that construction is
only .
In this paper, we make two important improvements over the result in
\cite{Li13b}. First, we construct an explicit extractor for \emph{three}
independent sources on bits with min-entropy .
In fact, our extractor works for one independent source with poly-logarithmic
min-entropy and another independent block source with two blocks each having
poly-logarithmic min-entropy. Thus, our result is nearly optimal, and the next
step would be to break the barrier in two-source extractors. Second, we
improve the error of the extractor from to
, which is almost optimal and crucial for cryptographic
applications. Some of the techniques developed here may be of independent
interests
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