Mass of Rotating Black Holes in Gauged Supergravities

The masses of several recently-constructed rotating black holes in gauged supergravities, including the general such solution in minimal gauged supergravity in five dimensions, have until now been calculated only by integrating the first law of thermodynamics. In some respects it is more satisfactory to have a calculation of the mass that is based directly upon the integration of a conserved quantity derived from a symmetry principal. In this paper, we evaluate the masses for the newly-discovered rotating black holes using the conformal definition of Ashtekar, Magnon and Das (AMD), and show that the results agree with the earlier thermodynamic calculations. We also consider the Abbott-Deser (AD) approach, and show that this yields an identical answer for the mass of the general rotating black hole in five-dimensional minimal gauged supergravity. In other cases we encounter discrepancies when applying the AD procedure. We attribute these to ambiguities or pathologies of the chosen decomposition into background AdS metric plus deviations when scalar fields are present. The AMD approach, involving no decomposition into background plus deviation, is not subject to such complications. Finally, we also calculate the Euclidean action for the five-dimensional solution in minimal gauged supergravity, showing that it is consistent with the quantum statistical relation.Comment: Typos corrected and references update

Transonic Elastic Model for Wiggly Goto-Nambu String

The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic string can be effectively represented by an elastic string model of exactly transonic type (with energy density $U$ inversely proportional to its tension $T$) is shown to have a firm mathematical basis.Comment: 8 pages, plain TeX, no figure

Phase conjugate fluorozirconate fibre laser operating at 800nm

We report phase-conjugate feedback into a fluorozirconate optical fiber amplifier at infrared wavelengths. By using a semiconductor laser diode at 807 nm, a grating is established in photorefractive BaTiO3 that, in the ring configuration, provides feedback into the amplifier necessary for laser action. Once written, the grating is self-sustaining, and lasing is observed even after the laser diode is removed

Pointed Hopf Algebras with classical Weyl Groups

We prove that Nichols algebras of irreducible Yetter-Drinfeld modules over classical Weyl groups $A \rtimes \mathbb S_n$ supported by $\mathbb S_n$ are infinite dimensional, except in three cases. We give necessary and sufficient conditions for Nichols algebras of Yetter-Drinfeld modules over classical Weyl groups $A \rtimes \mathbb S_n$ supported by $A$ to be finite dimensional.Comment: Combined with arXiv:0902.4748 plus substantial changes. To appear International Journal of Mathematic

A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge

In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate the Hamilton-Jacobi equation, showing that geodesic motion is integrable on this background. The separation of the Hamilton-Jacobi equation is intimately linked to the existence of an irreducible Killing tensor, which provides an extra constant of motion. We also demonstrate that the Klein-Gordon equation for this background is separable.Comment: LaTeX, 14 pages. v2: Typo corrected and equation added. v3: Reference added, introduction expanded, published versio

Separability in Cohomogeneity-2 Kerr-NUT-AdS Metrics

The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important role in the construction of generalisations of the Kerr metric, and in the uncovering of hidden symmetries associated with the existence of Killing tensors. In this paper, we show that the Hamilton-Jacobi and Klein-Gordon equations are separable in Kerr-AdS backgrounds in all dimensions, if one specialises the rotation parameters so that the metrics have cohomogeneity 2. Furthermore, we show that this property of separability extends to the NUT generalisations of these cohomogeneity-2 black holes that we obtained in a recent paper. In all these cases, we also construct the associated irreducible rank-2 Killing tensor whose existence reflects the hidden symmetry that leads to the separability. We also consider some cohomogeneity-1 specialisations of the new Kerr-NUT-AdS metrics, showing how they relate to previous results in the literature.Comment: Latex, 15 pages, minor typos correcte

Geometric scaling in high-energy QCD at nonzero momentum transfer

We show how one can obtain geometric scaling properties from the Balitsky-Kovchegov (BK) equation. We start by explaining how, this property arises for the b-independent BK equation. We show that it is possible to extend this model to the full BK equation including momentum transfer. The saturation scale behaves like max(q,Q_T) where q is the momentum transfer and Q_T a typical scale of the target.Comment: 4 pages, 2 figures. Talk given by G. Soyez at the "Rencontres de Moriond", 12-19 March 2005, La Thuile, Ital

Friction stir weld tools

A friction stir weld tool sleeve is supported by an underlying support pin. The pin material is preferably selected for toughness and fracture characteristics. The pin sleeve preferably has a geometry which employs the use of an interrupted thread, a plurality of flutes and/or eccentric path to provide greater flow through. Paddles have been found to assist in imparting friction and directing plastic metal during the welding process

Interaction between Faraday rotation and Cotton-Mouton effects in polarimetry modeling for NSTX

The evolution of electromagnetic wave polarization is modeled for propagation in the major radial direction in the National Spherical Torus Experiment (NSTX) with retroreflection from the center stack of the vacuum vessel. This modeling illustrates that the Cotton-Mouton effect-elliptization due to the magnetic field perpendicular to the propagation direction-is shown to be strongly weighted to the high-field region of the plasma. An interaction between the Faraday rotation and Cotton-Mouton effects is also clearly identified. Elliptization occurs when the wave polarization direction is neither parallel nor perpendicular to the local transverse magnetic field. Since Faraday rotation modifies the polarization direction during propagation, it must also affect the resultant elliptization. The Cotton-Mouton effect also intrinsically results in rotation of the polarization direction, but this effect is less significant in the plasma conditions modeled. The interaction increases at longer wavelength, and complicates interpretation of polarimetry measurements.Comment: Contributed paper published as part of the Proceedings of the 18th Topical Conference on High-Temperature Plasma Diagnostics, Wildwood, New Jersey, May, 201