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 ($\Lambda_c$) 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 $\Lambda_c$ and type III with $\Lambda_c=0$. It is shown that there are two, one and three distinct classes of solutions when $\Lambda_c$ 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 $P(\Lambda)$ of non-twisting, non-expanding type N solutions of vacuum Einstein equations with a cosmological constant $\Lambda$. We show that the only non-trivial waves of this type in Minkowski spacetime are impulsive pp-waves. For $\Lambda\not=0$ we demonstrate that the canonical subclasses of $P(\Lambda)$, 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