The Anti-Self-Dual Deformation Complex and a conjecture of Singer

Let $(M^4,g)$ be a smooth, closed, oriented anti-self-dual (ASD) four-manifold. $(M^4,g)$ is said to be unobstructed if the cokernel of the linearization of the self-dual Weyl tensor is trivial. This condition can also be characterized as the vanishing of the second cohomology group of the ASD deformation complex, and is central to understanding the local structure of the moduli space of ASD conformal structures. It also arises in construction of ASD manifolds by twistor and gluing methods. In this article we give conformally invariant conditions which imply an ASD manifold of positive Yamabe type is unobstructed

An LDEF 2 dust instrument for discrimination between orbital debris and natural particles in near-Earth space

The characteristics of a space dust instrument which would be ideally suited to carry out near-Earth dust measurements on a possible Long Duraction Exposure Facility reflight mission (LDEF 2) is discussed. As a model for the trajectory portion of the instrument proposed for LDEF 2, the characteristics of a SPAce DUSt instrument (SPADUS) currently under development for flight on the USA ARGOS mission to measure the flux, mass, velocity, and trajectory of near-Earth dust is summarized. Since natural (cosmic) dust and man-made dust particles (orbital debris) have different velocity and trajectory distributions, they are distinguished by means of the SPADUS velocity/trajectory information. The SPADUS measurements will cover the dust mass range approximately 5 x 10(exp -12) g (2 microns diameter) to approximately 1 x 10(exp -5) g (200 microns diameter), with an expected mean error in particle trajectory of approximately 7 deg (isotropic flux). Arrays of capture cell devices positioned behind the trajectory instrumentation would provide for Earth-based chemical and isotopic analysis of captured dust. The SPADUS measurement principles, characteristics, its role in the ARGOS mission, and its application to an LDEF 2 mission are summarized

A conformally invariant sphere theorem in four dimensions

In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 inequality of the Weyl tensor and positivity of the Yamabe invariant.Comment: 39 pages, 0 figure

On the stable configuration of ultra-relativistic material spheres. The solution for the extremely hot gas

During the last stage of collapse of a compact object into the horizon of events, the potential energy of its surface layer decreases to a negative value below all limits. The energy-conservation law requires an appearance of a positive-valued energy to balance the decrease. We derive the internal-state properties of the ideal gas situated in an extremely strong, ultra-relativistic gravitational field and suggest to apply our result to a compact object with the radius which is slightly larger than or equal to the Schwarzschild's gravitational radius. On the surface of the object, we find that the extreme attractivity of the gravity is accompanied with an extremely high internal, heat energy. This internal energy implies a correspondingly high pressure, the gradient of which has such a behavior that it can compete with the gravity. In a more detail, we find the equation of state in the case when the magnitude of the potential-type energy of constituting gas particles is much larger than their rest energy. This equation appears to be identical with the general-relativity condition of the equilibrium between the gravity and pressure gradient. The consequences of the identity are discussed.Comment: 12 pages (no figure, no table) Changes in 3-rd version: added an estimate of neutrino cooling and relative time-scale of the final stage of URMS collaps

The Observations Of The X-Ray Source Hz Herculis-Hercules X-1

NASAESASRCAstronom

Rotational symmetry of self-similar solutions to the Ricci flow

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.Comment: Final version, to appear in Invent. Mat

First Results from the X-ray and Optical Survey of the Chandra Deep Field South

We present our first results from 130 ks of X-ray observations obtained with the Advanced CCD Imaging Spectrometer on the Chandra X-ray Observatory. We reach a flux of 2 X 10^(-16) erg s^(-1) cm^(-2) in the 0.5-2 keV soft band and 2 X 10^(-15) erg s^(-1) cm^(-2) in the 2-10 keV hard band. For the optical identification we carried out a survey in VRI with the FORS-1 imaging-spectrometer on the ANTU telescope (UT-1 at VLT) complete to R <= 26. This dataset was complemented with data from the ESO Imaging Survey (EIS) in the UBJK bands and the ESO Wide Field Imager Survey (WFI) in the B band. The positional accuracy of the X-ray detections is of order of 1'' in the central 6'. Optical identifications are found for ~90% of the sources. We obtain the cumulative spectra of the faint and bright X-ray sources in the sample. A power law fit in the range 2-10 keV using the galactic value of N_H ~ 8 x 10^(19) cm^(-2), yields a photon index of Gamma = 1.70+-0.06 and 1.35+-0.10 for the bright and faint sample respectively, showing a flattening of the spectrum at lower fluxes. We discuss the LogN-LogS relationship and the discrete source contribution to the integrated X-ray sky flux. In the soft band, the sources now detected at fluxes below 10^(-15) erg s^(-1) cm^(-2) contribute (4.0 +- 0.3) X 10^(-12) erg cm^(-2)s^(-1) deg^(-2) to the total XRB. The flux resolved in the hard band down to the flux limit of 2 X 10^(-15) erg s^(-1) cm^(-2) now contributes a total of 1.6 X 10^(-11) erg cm^(-2) s^(-1) deg^(-2) which amounts to a fraction of 60-80% of the total measured background. This result confirms that the XRB is due to the integrated contribution of discrete sources, but shows that there is still a relevant fraction (at least 20%) of the hard XRB to be resolved at fluxes below 10^(-15) erg s^(-1) cm^(-2). (ABRIDGED)Comment: 25 pages, 9 figures, ApJ submitte