183 research outputs found
A Model for the Moving `Wisps' in the Crab Nebula
I propose that the moving `wisps' near the center of the Crab Nebula result
from nonlinear Kelvin-Helmholtz instabilities in the equatorial plane of the
shocked pulsar wind. Recent observations suggest that the wisps trace out
circular wavefronts in this plane, expanding radially at speeds approximately
less than c/3. Instabilities could develop if there is sufficient velocity
shear between a faster-moving equatorial zone and a slower moving shocked
pulsar wind at higher latitudes. The development of shear could be related to
the existence of a neutral sheet -- with weak magnetic field -- in the
equatorial zone, and could also be related to a recent suggestion by Begelman
that the magnetic field in the Crab pulsar wind is much stronger than had been
thought. I show that plausible conditions could lead to the growth of
instabilities at the radii and speeds observed, and that their nonlinear
development could lead to the appearance of sharp wisplike features.Comment: 7 pages; 3 postscript figures; LaTex, uses emulateapj.sty; to Appear
in the Astrophysical Journal, Feb. 20, 1999, Vol. 51
Generalised Kundt waves and their physical interpretation
We present the complete family of space-times with a non-expanding,
shear-free, twist-free, geodesic principal null congruence (Kundt waves) that
are of algebraic type III and for which the cosmological constant ()
is non-zero. The possible presence of an aligned pure radiation field is also
assumed. These space-times generalise the known vacuum solutions of type N with
arbitrary and type III with . It is shown that there
are two, one and three distinct classes of solutions when is
respectively zero, positive and negative. The wave surfaces are plane,
spherical or hyperboloidal in Minkowski, de Sitter or anti-de Sitter
backgrounds respectively, and the structure of the family of wave surfaces in
the background space-time is described. The weak singularities which occur in
these space-times are interpreted in terms of envelopes of the wave surfaces.Comment: 16 pages including 2 figures. To appear in Classical and Quantum Gra
General approach to the study of vacuum space-times with an isometry
In vacuum space-times the exterior derivative of a Killing vector field is a
2-form (named here as the Papapetrou field) that satisfies Maxwell's equations
without electromagnetic sources. In this paper, using the algebraic structure
of the Papapetrou field, we will set up a new formalism for the study of vacuum
space-times with an isometry, which is suitable to investigate the connections
between the isometry and the Petrov type of the space-time. This approach has
some advantages, among them, it leads to a new classification of these
space-times and the integrability conditions provide expressions that determine
completely the Weyl curvature. These facts make the formalism useful for
application to any problem or situation with an isometry and requiring the
knowledge of the curvature.Comment: 24 pages, LaTeX2e, IOP style. To appear in Classical and Quantum
Gravit
Late Time Tail of Wave Propagation on Curved Spacetime
The late time behavior of waves propagating on a general curved spacetime is
studied. The late time tail is not necessarily an inverse power of time. Our
work extends, places in context, and provides understanding for the known
results for the Schwarzschild spacetime. Analytic and numerical results are in
excellent agreement.Comment: 11 pages, WUGRAV-94-1
Formal analogies between gravitation and electrodynamics
We develop a theoretical framework that allows us to compare electromagnetism
and gravitation in a fully covariant way. This new scenario does not rely on
any kind of approximation nor associate objects with different operational
meaning as it's sometime done in the literature. We construct the
electromagnetic analogue to the Riemann and Weyl tensors and develop the
equations of motion for these objects. In particular, we are able to identify
precisely how and in what conditions gravity can be mapped to electrodynamics.
As a consequence, many of the gemometrical tools of General Relativity can be
applied to Electromagnetism and vice-versa. We hope our results would shed new
light in the nature of electromagnetic and gravitational theories.Comment: 9pages, submitted to General Relativity and Gravitatio
Geodesic motion in the Kundt spacetimes and the character of envelope singularity
We investigate geodesics in specific Kundt type N (or conformally flat)
solutions to Einstein's equations. Components of the curvature tensor in
parallelly transported tetrads are then explicitly evaluated and analyzed. This
elucidates some interesting global properties of the spacetimes, such as an
inherent rotation of the wave-propagation direction, or the character of
singularities. In particular, we demonstrate that the characteristic envelope
singularity of the rotated wave-fronts is a (non-scalar) curvature singularity,
although all scalar invariants of the Riemann tensor vanish there.Comment: 21 pages, 3 figures. To appear in Class. Quantum Gra
Non-expanding impulsive gravitational waves
We investigate a class of impulsive gravitational waves which propagate
either in Minkowski or in the (anti-)de Sitter background. These waves are
constructed as impulsive members of the Kundt class of
non-twisting, non-expanding type N solutions of vacuum Einstein equations with
a cosmological constant . We show that the only non-trivial waves of
this type in Minkowski spacetime are impulsive pp-waves. For we
demonstrate that the canonical subclasses of , which are
invariantly different for smooth profiles, are all locally equivalent for
impulsive profiles. Also, we present coordinate system for these impulsive
solutions which is explicitly continuous.Comment: 12 pages, to appear in Class. Quantum Gra
Charged Annular Disks and Reissner-Nordstr\"{o}m Type Black Holes from Extremal Dust
We present the first analytical superposition of a charged black hole with an
annular disk of extremal dust. In order to obtain the solutions, we first solve
the Einstein-Maxwell field equations for sources that represent disk-like
configurations of matter in confomastatic spacetimes by assuming a functional
dependence among the metric function, the electric potential and an auxiliary
function,which is taken as a solution of the Laplace equation. We then employ
the Lord Kelvin Inversion Method applied to models of finite extension in order
to obtain annular disks. The structures obtained extend to infinity, but their
total masses are finite and all the energy conditions are satisfied. Finally,
we observe that the extremal Reissner-Nordstr\"{o}m black hole can be embedded
into the center of the disks by adding a boundary term in the inversion.Comment: 17 revtex pages, 8 eps figure
Wigner Trajectory Characteristics in Phase Space and Field Theory
Exact characteristic trajectories are specified for the time-propagating
Wigner phase-space distribution function. They are especially simple---indeed,
classical---for the quantized simple harmonic oscillator, which serves as the
underpinning of the field theoretic Wigner functional formulation introduced.
Scalar field theory is thus reformulated in terms of distributions in field
phase space. Applications to duality transformations in field theory are
discussed.Comment: 9 pages, LaTex2
Explicit Kundt type II and N solutions as gravitational waves in various type D and O universes
A particular yet large class of non-diverging solutions which admits a
cosmological constant, electromagnetic field, pure radiation and/or general
non-null matter component is explicitly presented. These spacetimes represent
exact gravitational waves of arbitrary profiles which propagate in background
universes such as Minkowski, conformally flat (anti-)de Sitter, Edgar-Ludwig,
Bertotti-Robinson, and type D (anti-)Nariai or Plebanski-Hacyan spaces, and
their generalizations. All possibilities are discussed and are interpreted
using a unifying simple metric form. Sandwich and impulsive waves propagating
in the above background spaces with different geometries and matter content can
easily be constructed. New solutions are identified, e.g. type D pure radiation
or explicit type II electrovacuum waves in (anti-)Nariai universe. It is also
shown that, in general, there are no conformally flat Einstein-Maxwell fields
with a non-vanishing cosmological constant.Comment: 17 pages, LaTeX 2e. v2: added two references concerning generalized
Kerr-Schild transformations, minor changes in the tex
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