Sharp version of the Goldberg-Sachs theorem

We reexamine from first principles the classical Goldberg-Sachs theorem from General Relativity. We cast it into the form valid for complex metrics, as well as real metrics of any signature. We obtain the sharpest conditions on the derivatives of the curvature that are sufficient for the implication (integrability of a field of alpha planes)$\Rightarrow$(algebraic degeneracy of the Weyl tensor). With every integrable field of alpha planes we associate a natural connection, in terms of which these conditions have a very simple form.Comment: In this version we made a minor change in Remark 5.5 and simplified Section 6, starting at Theorem 6.

Implications of the HERA Events for the R-Parity Breaking SUSY Signals at Tevatron

The favoured R-parity violating SUSY scenarios for the anomalous HERA events correspond to top and charm squark production via the $\lambda'_{131}$ and $\lambda'_{121}$ couplings. In both cases the corresponding electronic branching fractions of the squarks are expected to be $\ll 1$. Consequently the canonical leptoquark signature is incapable of probing these scenarios at the Tevatron collider over most of the MSSM parameter space. We suggest alternative signatures for probing them at Tevatron, which seem to be viable over the entire range of MSSM parameters.Comment: 20 pages Latex file with 4 ps files containing 4 figure

Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder

The effect of a weak three-dimensional (3d) isotropic laser speckle disorder on various thermodynamic properties of a dilute Bose gas is considered at zero temperature. First, we summarize the derivation of the autocorrelation function of laser speckles in 1d and 2d following the seminal work of Goodman. The goal of this discussion is to show that a Gaussian approximation of this function, proposed in some recent papers, is inconsistent with the general background of laser speckle theory. Then we propose a possible experimental realization for an isotropic 3d laser speckle potential and derive its corresponding autocorrelation function. Using a Fourier transform of that function, we calculate both condensate depletion and sound velocity of a Bose-Einstein condensate as disorder ensemble averages of such a weak laser speckle potential within a perturbative solution of the Gross-Pitaevskii equation. By doing so, we reproduce the expression of the normalfluid density obtained earlier within the treatment of Landau. This physically transparent derivation shows that condensate particles, which are scattered by disorder, form a gas of quasiparticles which is responsible for the normalfluid component

Domain Wall Spacetimes: Instability of Cosmological Event and Cauchy Horizons

The stability of cosmological event and Cauchy horizons of spacetimes associated with plane symmetric domain walls are studied. It is found that both horizons are not stable against perturbations of null fluids and massless scalar fields; they are turned into curvature singularities. These singularities are light-like and strong in the sense that both the tidal forces and distortions acting on test particles become unbounded when theses singularities are approached.Comment: Latex, 3 figures not included in the text but available upon reques

Helicity Analysis of Semileptonic Hyperon Decays Including Lepton Mass Effects

Using the helicity method we derive complete formulas for the joint angular decay distributions occurring in semileptonic hyperon decays including lepton mass and polarization effects. Compared to the traditional covariant calculation the helicity method allows one to organize the calculation of the angular decay distributions in a very compact and efficient way. In the helicity method the angular analysis is of cascade type, i.e. each decay in the decay chain is analyzed in the respective rest system of that particle. Such an approach is ideally suited as input for a Monte Carlo event generation program. As a specific example we take the decay $\Xi^0 \to \Sigma^+ + l^- + \bar{\nu}_l$ ($l^-=e^-, \mu^-$) followed by the nonleptonic decay $\Sigma^+ \to p + \pi^0$ for which we show a few examples of decay distributions which are generated from a Monte Carlo program based on the formulas presented in this paper. All the results of this paper are also applicable to the semileptonic and nonleptonic decays of ground state charm and bottom baryons, and to the decays of the top quark.Comment: Published version. 40 pages, 11 figures included in the text. Typos corrected, comments added, references added and update

X-wave mediated instability of plane waves in Kerr media

Plane waves in Kerr media spontaneously generate paraxial X-waves (i.e. non-dispersive and non-diffractive pulsed beams) that get amplified along propagation. This effect can be considered a form of conical emission (i.e. spatio-temporal modulational instability), and can be used as a key for the interpretation of the out of axis energy emission in the splitting process of focused pulses in normally dispersive materials. A new class of spatio-temporal localized wave patterns is identified. X-waves instability, and nonlinear X-waves, are also expected in periodical Bose condensed gases.Comment: 4 pages, 6 figure

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations

In melt-blowing very thin liquid fiber jets are spun due to high-velocity air streams. In literature there is a clear, unsolved discrepancy between the measured and computed jet attenuation. In this paper we will verify numerically that the turbulent velocity fluctuations causing a random aerodynamic drag on the fiber jets -- that has been neglected so far -- are the crucial effect to close this gap. For this purpose, we model the velocity fluctuations as vector Gaussian random fields on top of a k-epsilon turbulence description and develop an efficient sampling procedure. Taking advantage of the special covariance structure the effort of the sampling is linear in the discretization and makes the realization possible

Observing the First Stars and Black Holes

The high sensitivity of JWST will open a new window on the end of the cosmological dark ages. Small stellar clusters, with a stellar mass of several 10^6 M_sun, and low-mass black holes (BHs), with a mass of several 10^5 M_sun should be directly detectable out to redshift z=10, and individual supernovae (SNe) and gamma ray burst (GRB) afterglows are bright enough to be visible beyond this redshift. Dense primordial gas, in the process of collapsing from large scales to form protogalaxies, may also be possible to image through diffuse recombination line emission, possibly even before stars or BHs are formed. In this article, I discuss the key physical processes that are expected to have determined the sizes of the first star-clusters and black holes, and the prospect of studying these objects by direct detections with JWST and with other instruments. The direct light emitted by the very first stellar clusters and intermediate-mass black holes at z>10 will likely fall below JWST's detection threshold. However, JWST could reveal a decline at the faint-end of the high-redshift luminosity function, and thereby shed light on radiative and other feedback effects that operate at these early epochs. JWST will also have the sensitivity to detect individual SNe from beyond z=10. In a dedicated survey lasting for several weeks, thousands of SNe could be detected at z>6, with a redshift distribution extending to the formation of the very first stars at z>15. Using these SNe as tracers may be the only method to map out the earliest stages of the cosmic star-formation history. Finally, we point out that studying the earliest objects at high redshift will also offer a new window on the primordial power spectrum, on 100 times smaller scales than probed by current large-scale structure data.Comment: Invited contribution to "Astrophysics in the Next Decade: JWST and Concurrent Facilities", Astrophysics & Space Science Library, Eds. H. Thronson, A. Tielens, M. Stiavelli, Springer: Dordrecht (2008