Generic metrics and the mass endomorphism on spin three-manifolds

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an analogy to the mass in the Yamabe problem. We show that the mass endomorphism of a generic metric on a three-dimensional spin manifold is nonzero. This implies a strict inequality which can be used to avoid bubbling-off phenomena in conformal spin geometry.Comment: 8 page

Bunburra Rockhole: Exploring the geology of a new differentiated asteroid

Bunburra Rockhole is the first recovered meteorite of the Desert Fireball Network. We expanded a bulk chemical study of the Bunburra Rockhole meteorite to include major, minor and trace element analyses, as well as oxygen and chromium isotopes, in several different pieces of the meteorite. This was to determine the extent of chemical heterogeneity and constrain the origin of the meteorite. Minor and trace element analyses in all pieces are exactly on the basaltic eucrite trend. Major element analyses show a slight deviation from basaltic eucrite compositions, but not in any systematic pattern. New oxygen isotope analyses on 23 pieces of Bunburra Rockhole shows large variation in both δ17O and δ18O, and both are well outside the HED parent body fractionation line. We present the first Cr isotope results of this rock, which are also distinct from HEDs. Detailed computed tomographic scanning and back-scattered electron mapping do not indicate the presence of any other meteoritic contaminant (contamination is also unlikely based on trace element chemistry). We therefore conclude that Bunburra Rockhole represents a sample of a new differentiated asteroid, one that may have more variable oxygen isotopic compositions than 4 Vesta. The fact that Bunburra Rockhole chemistry falls on the eucrite trend perhaps suggests that multiple objects with basaltic crusts accreted in a similar region of the Solar System

Geometrization of metric boundary data for Einstein's equations

The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new formulation of constraint-preserving boundary conditions of the Sommerfeld type has recently been established for such systems. In this paper these boundary conditions are recast in a geometric form. This serves as a first step toward their application to other metric formulations of Einstein's equations.Comment: Article to appear in Gen. Rel. Grav. volume in memory of Juergen Ehler

Initial data for a head on collision of two Kerr-like black holes with close limit

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. This family of initial data has the following properties: (i) When the mass parameter of one of them is zero or when the distance between them goes to infinity, it reduces exactly to the Kerr initial data. (ii) When the distance between them is zero, we obtain exactly a Kerr initial data with mass and angular momentum equal to the sum of the mass and angular momentum parameters of each of them. The initial data depends smoothly on the distance, the mass and the angular momentum parameters.Comment: 15 pages, no figures, Latex2

Conformal structures of static vacuum data

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null infinity obstructs the development of a smooth conformal structure at null infinity. For the solution-jets arising from time reflection symmetric data to extend smoothly to the critical sets it is necessary that the Cotton tensor of the initial three-metric h satisfies a certain conformally invariant condition (*) at space-like infinity, it is sufficient that h be asymptotically static at space-like infinity. The purpose of this article is to characterize the gap between these conditions. We show that with the class of metrics which satisfy condition (*) on the Cotton tensor and a certain non-degeneracy requirement is associated a one-form $\kappa$ with conformally invariant differential $d\kappa$. We provide two criteria: If $h$ is real analytic, $\kappa$ is closed, and one of it integrals satisfies a certain equation then h is conformal to static data near space-like infinity. If h is smooth, $\kappa$ is asymptotically closed, and one of it integrals satisfies a certain equation asymptotically then h is asymptotically conformal to static data at space-like infinity.Comment: 68 pages, typos corrected, references and details adde

Symmetric hyperbolic systems for a large class of fields in arbitrary dimension

Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance of the so-called "superenergy" tensors, which provide the necessary symmetric positive matrices, is emphasized and made explicit. Thereby, a unified treatment of many physical systems is achieved, as well as of the sometimes called "higher order" systems. The characteristics of these symmetric hyperbolic systems are always physical, and directly related to the null directions of the superenergy tensor, which are in particular principal null directions of the tensor field solutions. Generic energy estimates and inequalities are presented too.Comment: 24 pages, no figure

Observation of diffractive orbits in the spectrum of excited NO in a magnetic field

We investigate the experimental spectra of excited NO molecules in the diamagnetic regime and develop a quantitative semiclassical framework to account for the results. We show the dynamics can be interpreted in terms of classical orbits provided that in addition to the geometric orbits, diffractive effects are appropriately taken into account. We also show how individual orbits can be extracted from the experimental signal and use this procedure to reveal the first experimental manifestation of inelastic diffractive orbits.Comment: 4 fig

The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence

We calculate the volumes of a large class of Einstein manifolds, namely Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones described by polynomial embedding relations in C^n. These volumes are important because they allow us to extend and test the AdS/CFT correspondence. We use these volumes to extend the central charge calculation of Gubser (1998) to the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These volumes also allow one to quantize precisely the D-brane flux of the AdS supergravity solution. We end by demonstrating a relationship between the volumes of these Einstein spaces and the number of holomorphic polynomials (which correspond to chiral primary operators in the field theory dual) on the corresponding affine cone.Comment: 25 pp, LaTeX, 1 figure, v2: refs adde

Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein's equations

We present new many-parameter families of strongly and symmetric hyperbolic formulations of Einstein's equations that include quite general algebraic and live gauge conditions for the lapse. The first system that we present has 30 variables and incorporates an algebraic relationship between the lapse and the determinant of the three metric that generalizes the densitized lapse prescription. The second system has 34 variables and uses a family of live gauges that generalizes the Bona-Masso slicing conditions. These systems have free parameters even after imposing hyperbolicity and are expected to be useful in 3D numerical evolutions. We discuss under what conditions there are no superluminal characteristic speeds

Dibaryon Spectroscopy

The AdS/CFT correspondence relates dibaryons in superconformal gauge theories to holomorphic curves in Kaehler-Einstein surfaces. The degree of the holomorphic curves is proportional to the gauge theory conformal dimension of the dibaryons. Moreover, the number of holomorphic curves should match, in an appropriately defined sense, the number of dibaryons. Using AdS/CFT backgrounds built from the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999), we show that the gauge theory prediction for the dimension of dibaryonic operators does indeed match the degree of the corresponding holomorphic curves. For AdS/CFT backgrounds built from cones over del Pezzo surfaces, we are able to match the degree of the curves to the conformal dimension of dibaryons for the n'th del Pezzo surface, n=1,2,...,6. Also, for the del Pezzos and the A_k type generalized conifolds, for the dibaryons of smallest conformal dimension, we are able to match the number of holomorphic curves with the number of possible dibaryon operators from gauge theory.Comment: 30 pages, 6 figures, corrected refs; v3 typos correcte