2,978 research outputs found

    The Jang equation reduction of the spacetime positive energy theorem in dimensions less than eight

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    We extend the Jang equation proof of the positive energy theorem due to R. Schoen and S.-T. Yau from dimension n=3n=3 to dimensions 3n<83 \leq n <8. This requires us to address several technical difficulties that are not present when n=3n=3. The regularity and decay assumptions for the initial data sets to which our argument applies are weaker than those of R. Schoen and S.-T. Yau. In recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a different proof of the full positive mass theorem in dimensions 3n<83 \leq n < 8. We pointed out that this theorem can alternatively be derived from our density argument and the positive energy theorem of the present paper.Comment: All comments welcome! Final version to appear in Comm. Math. Phy

    A generalization of Hawking's black hole topology theorem to higher dimensions

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    Hawking's theorem on the topology of black holes asserts that cross sections of the event horizon in 4-dimensional asymptotically flat stationary black hole spacetimes obeying the dominant energy condition are topologically 2-spheres. This conclusion extends to outer apparent horizons in spacetimes that are not necessarily stationary. In this paper we obtain a natural generalization of Hawking's results to higher dimensions by showing that cross sections of the event horizon (in the stationary case) and outer apparent horizons (in the general case) are of positive Yamabe type, i.e., admit metrics of positive scalar curvature. This implies many well-known restrictions on the topology, and is consistent with recent examples of five dimensional stationary black hole spacetimes with horizon topology S2×S1S^2 \times S^1. The proof is inspired by previous work of Schoen and Yau on the existence of solutions to the Jang equation (but does not make direct use of that equation).Comment: 8 pages, latex2e, references updated, minor corrections, to appear in Communications in Mathematical Physic

    Existence, Regularity, and Properties of Generalized Apparent Horizons

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    We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.Comment: 16 pages, thoroughly revised, no major changes, to appear in Comm. Math. Phy

    Positive mass theorem for the Paneitz-Branson operator

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    We prove that under suitable assumptions, the constant term in the Green function of the Paneitz-Branson operator on a compact Riemannian manifold (M,g)(M,g) is positive unless (M,g)(M,g) is conformally diffeomophic to the standard sphere. The proof is inspired by the positive mass theorem on spin manifolds by Ammann-Humbert.Comment: 7 page

    Gluing Initial Data Sets for General Relativity

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    We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically and physically natural. Secondly, the construction is completely local in the sense that the initial data is left unaltered on the complement of arbitrarily small neighborhoods of the points about which the gluing takes place. Using this construction we establish the existence of cosmological, maximal globally hyperbolic, vacuum space-times with no constant mean curvature spacelike Cauchy surfaces.Comment: Final published version - PRL, 4 page

    Advanced composite applications for sub-micron biologically derived microstructures

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    A major thrust of advanced material development is in the area of self-assembled ultra-fine particulate based composites (micro-composites). The application of biologically derived, self-assembled microstructures to form advanced composite materials is discussed. Hollow 0.5 micron diameter cylindrical shaped microcylinders self-assemble from diacetylenic lipids. These microstructures have a multiplicity of potential applications in the material sciences. Exploratory development is proceeding in application areas such as controlled release for drug delivery, wound repair, and biofouling as well as composites for electronic and magnetic applications, and high power microwave cathodes

    Perturbative Solutions of the Extended Constraint Equations in General Relativity

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    The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface ZZ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on ZZ, and are equivalent to the usual constraint equations that ZZ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.Comment: This third and final version has been accepted for publication in Communications in Mathematical Physic

    Results of special mechanical analyses of Luna 16 material

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    The studies carried out on the Luna 16 regolith have confirmed the data that were already published internationally. By means of activation analysis under irradiation in the reactor, activation analysis with a 14 MeV U-generator, and mass spectroscopy on samples of 10 or 20 mg, six main and 63 trace elements were quantitatively determined and compared with known data

    Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT

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    The anti--de Sitter/conformal field theory (AdS/CFT) correspondence is a powerful tool that promises to provide new insights toward a full understanding of field theories under extreme conditions, including but not limited to quark-gluon plasma, Fermi liquid and superconductor. In many such applications, one typically models the field theory with asymptotically AdS black holes. These black holes are subjected to stringy effects that might render them unstable. Ho\v{r}ava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attentions due to its power-counting renormalizability. In terms of AdS/CFT correspondence, Ho\v{r}ava-Lifshitz black holes might be useful to model holographic superconductors with Lifshitz scaling symmetry. It is thus interesting to study the stringy stability of Ho\v{r}ava-Lifshitz black holes in the context of AdS/CFT. We find that uncharged topological black holes in λ=1\lambda=1 Ho\v{r}ava-Lifshitz theory are nonperturbatively stable, unlike their counterparts in Einstein gravity, with the possible exceptions of negatively curved black holes with detailed balance parameter ϵ\epsilon close to unity. Sufficiently charged flat black holes for ϵ\epsilon close to unity, and sufficiently charged positively curved black holes with ϵ\epsilon close to zero, are also unstable. The implication to the Ho\v{r}ava-Lifshitz holographic superconductor is discussed.Comment: 15 pages, 6 figures. Updated version accepted by Phys. Rev. D, with corrections to various misprints. References update

    Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data

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    We establish necessary conditions for the appearance of both apparent horizons and singularities in the initial data of spherically symmetric general relativity when spacetime is foliated extrinsically. When the dominant energy condition is satisfied these conditions assume a particularly simple form. Let ρMax\rho_{Max} be the maximum value of the energy density and \ell the radial measure of its support. If ρMax2\rho_{Max}\ell^2 is bounded from above by some numerical constant, the initial data cannot possess an apparent horizon. This constant does not depend sensitively on the gauge. An analogous inequality is obtained for singularities with some larger constant. The derivation exploits Poincar\'e type inequalities to bound integrals over certain spatial scalars. A novel approach to the construction of analogous necessary conditions for general initial data is suggested.Comment: 15 pages, revtex, to appear in Phys. Rev.
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