3,746 research outputs found

    Fertilizers for Ohio Farms

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    A note on a third order curvature invariant in static spacetimes

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    We consider here the third order curvature invariant I=Rμνρσ;δRμνρσ;δI=R_{\mu\nu\rho\sigma;\delta}R^{\mu\nu\rho\sigma;\delta} in static spacetimes M=R×Σ{\cal M}=R\times\Sigma for which Σ\Sigma is conformally flat. We evaluate explicitly the invariant for the NN-dimensional Majumdar-Papapetrou multi black-holes solution, confirming that II does indeed vanish on the event horizons of such black-holes. Our calculations show, however, that solely the vanishing of II is not sufficient to locate an event horizon in non-spherically symmetric spacetimes. We discuss also some tidal effects associated to the invariant II.Comment: 5 pages, 3 figures. Extra material available at http://vigo.ime.unicamp.br/in

    Rotating solenoidal perfect fluids of Petrov type D

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    We prove that aligned Petrov type D perfect fluids for which the vorticity vector is not orthogonal to the plane of repeated principal null directions and for which the magnetic part of the Weyl tensor with respect to the fluid velocity has vanishing divergence, are necessarily purely electric or locally rotationally symmetric. The LRS metrics are presented explicitly.Comment: 6 pages, no figure

    Those wonderful elastic waves

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    We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic media from a free surface is shown to be characterized by three critical angles.Comment: 11 Figures 26 page

    The Application of the Newman-Janis Algorithm in Obtaining Interior Solutions of the Kerr Metric

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    In this paper we present a class of metrics to be considered as new possible sources for the Kerr metric. These new solutions are generated by applying the Newman-Janis algorithm (NJA) to any static spherically symmetric (SSS) ``seed'' metric. The continuity conditions for joining any two of these new metrics is presented. A specific analysis of the joining of interior solutions to the Kerr exterior is made. The boundary conditions used are those first developed by Dormois and Israel. We find that the NJA can be used to generate new physically allowable interior solutions. These new solutions can be matched smoothly to the Kerr metric. We present a general method for finding such solutions with oblate spheroidal boundary surfaces. Finally a trial solution is found and presented.Comment: 11 pages, Latex, 4 postscript figures. To be published in Classical and Quantum Gravity. Title and abstract are now on the same pag
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