Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry

We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler metrics with vanishing scalar curvature which are invariant under the conformal action of Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem with two double poles. The resulting metrics are non-diagonal in the left-invariant basis and are explicitly given in terms of Bessel functions and their integrals. We also make a connection with the LeBrun ansatz, and characterise the associated solutions of the SU(\infty) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.Comment: Dedicated to Maciej Przanowski on the occasion of his 65th birthday. Minor corrections. To appear in CQ

Collapsing Shells and the Isoperimetric Inequality for Black Holes

Recent results of Trudinger on Isoperimetric Inequalities for non-convex bodies are applied to the gravitational collapse of a lightlike shell of matter to form a black hole. Using some integral identities for co-dimension two surfaces in Minkowski spacetime, the area $A$ of the apparent horizon is shown to be bounded above in terms of the mass $M$ by the $16 \pi G^2 M^2$, which is consistent with the Cosmic Censorship Hypothesis. The results hold in four spacetime dimensions and above.Comment: 16 pages plain TE

Harmonic functions, central quadrics, and twistor theory

Solutions to the $n$-dimensional Laplace equation which are constant on a central quadric are found. The associated twistor description of the case $n=3$ is used to characterise Gibbons-Hawking metrics with tri-holomorphic SL(2, \C) symmetry.Comment: Final version. To appear in CQ

Einstein--Maxwell--Dilaton metrics from three--dimensional Einstein--Weyl structures

A class of time dependent solutions to $(3+1)$ Einstein--Maxwell-dilaton theory with attractive electric force is found from Einstein--Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and $SU(\infty)$ Toda equations. These solutions are obtained from time--like Kaluza--Klein reductions of $(3+2)$ solitons.Comment: 12 pages, to be published in Class.Quantum Gra

Gravitating defects of codimension-two

Thin gravitating defects with conical singularities in higher codimensions and with generalized Israel matching conditions are known to be inconsistent for generic energy-momentum. A way to remove this inconsistency is proposed and is realized for an axially symmetric gravitating codimension-two defect in six dimensional Einstein gravity. By varying with respect to the brane embedding fields, alternative matching conditions are derived, which are generalizations of the Nambu-Goto equations of motion of the defect, consistent with bulk gravity. For a maximally symmetric defect the standard picture is recovered. The four-dimensional perfect fluid cosmology coincides with conventional FRW in the case of radiation, but for dust it has rho^{4/3} instead of rho. A four-dimensional black hole solution is presented having the Schwarzschild form with a short-distance correction r^{-2}.Comment: Minor changes, to appear in Classical and Quantum Gravit

Trapped Surfaces in Vacuum Spacetimes

An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric case considered previously, to the case of maximal slices. The resulting theorem shows rigorously that there exists a large class of initial configurations for non-time symmetric pure gravitational waves satisfying the assumptions of the Penrose singularity theorem and so must have a singularity to the future.Comment: 14 page

Global Topology and Local Violation of Discrete Symmetries

Cosmological models that are locally consistent with general relativity and the standard model in which an object transported around the universe undergoes P, C and CP transformations, are constructed. This leads to generalization of the gauge fields that describe electro-weak and strong interactions by enlarging the gauge groups to include anti-unitary transformations. Gedanken experiments show that if all interactions obey Einstein causality then P, C and CP cannot be violated in these models. But another model, which would violate charge superselection rule even for an isolated system, is allowed. It is suggested that the fundamental physical laws must have these discrete symmetries which are broken spontaneously, or they must be non causal.Comment: 12 pages, 1 figure, latex, Revtex. Charge conjugation which is physically implemented in a cosmology with the appropriate topology is described in more detail. Some minor errors are corrected. Shortened to meet the page limit of Physical Review Letters to which this paper was submitte

RXTE Observations of 1A 1744-361: Correlated Spectral and Timing Behavior

We analyze Rossi X-ray Timing Explorer (RXTE) Proportional Counter Array (PCA) data of the transient low mass X-ray binary (LMXB) system 1A 1744-361. We explore the X-ray intensity and spectral evolution of the source, perform timing analysis, and find that 1A 1744-361 shows `atoll' behavior during the outbursts. The color-color diagram indicates that this LMXB was observed in a low intensity spectrally hard (low-hard) state and in a high intensity `banana' state. The low-hard state shows a horizontal pattern in the color-color diagram, and the previously reported `dipper QPO' appears only during this state. We also perform energy spectral analyses, and report the first detection of broad iron emission line and iron absorption edge from 1A 1744-361.Comment: 20 pages, 4 tables, 4 figures, accepted for publication in Ap

Proteasomal Interference Prevents Zona Pellucida Penetration and Fertilization in Mammals

doi: 10.1095/biolreprod.104.032532The ubiquitin-proteasome pathway has been implicated in the penetration of ascidian vitelline envelope by the fertilizing spermatozoon (Sawada et al., Proc Natl Acad Sci U S A 2002; 99:1223-1228). The present study provides experimental evidence demonstrating proteasome involvement in the penetration of mammalian zona pellucida (ZP). Using porcine in vitro fertilization as a model, penetration of ZP was completely inhibited by specific proteasomal inhibitors MG-132 and lactacystin. Three commercial rabbit sera recognizing 20S proteasomal core subunits b-1i, b-2i, a-6, and b-5 completely blocked fertilization at a very low concentration (i.e., diluted 1/2000 to 1/8000 in fertilization medium). Neither proteasome inhibitors nor antibodies had any effects on sperm-ZP binding and acrosome exocytosis in zona-enclosed oocytes or on fertilization rates in zona-free oocytes, which were highly polyspermic. Consistent with a possible role of ubiquitin-proteasome pathway in ZP penetration, ubiquitin and various a and b type proteasomal subunits were detected in boar sperm acrosome by specific antibodies, immunoprecipitated and microsequenced by MALDITOF from boar sperm extracts. Antiubiquitin-immunoreactive substrates were detected on the outer face of ZP by epifluorescence microscopy. This study therefore provides strong evidence implicating the ubiquitin-proteasome pathway in mammalian fertilization and zona penetration. This finding opens a new line of acrosome/ZP research because further studies of the sperm acrosomal proteasome can provide new tools for the management of polyspermia during in vitro fertilization and identify new targets for contraceptive development

Mapping the G-structures and supersymmetric vacua of five-dimensional N=4 supergravity

We classify the supersymmetric vacua of N=4, d=5 supergravity in terms of G-structures. We identify three classes of solutions: with R^3, SU(2) and generic SO(4) structure. Using the Killing spinor equations, we fully characterize the first two classes and partially solve the latter. With the N=4 graviton multiplet decomposed in terms of N=2 multiplets: the graviton, vector and gravitino multiplets, we obtain new supersymmetric solutions corresponding to turning on fields in the gravitino multiplet. These vacua are described in terms of an SO(5) vector sigma-model coupled with gravity, in three or four dimensions. A new feature of these N=4 vacua, which is not seen from an N=2 point of view, is the possibility for preserving more exotic fractions of supersymmetry. We give a few concrete examples of these new supersymmetric (albeit singular) solutions. Additionally, we show how by truncating the N=4, d=5 set of fields to minimal supergravity coupled with one vector multiplet we recover the known two-charge solutions.Comment: 31 pages, late