5,885 research outputs found

    A Covariant Entropy Conjecture

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    We conjecture the following entropy bound to be valid in all space-times admitted by Einstein's equation: Let A be the area of any two-dimensional surface. Let L be a hypersurface generated by surface-orthogonal null geodesics with non-positive expansion. Let S be the entropy on L. Then S does not exceed A/4. We present evidence that the bound can be saturated, but not exceeded, in cosmological solutions and in the interior of black holes. For systems with limited self-gravity it reduces to Bekenstein's bound. Because the conjecture is manifestly time reversal invariant, its origin cannot be thermodynamic, but must be statistical. Thus it places a fundamental limit on the number of degrees of freedom in nature.Comment: 41 pages, 7 figures. v2,v3: references adde

    Dirac equation for embedded 4-geometries

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    We apply Dirac's square root idea to constraints for embedded 4-geometries swept by a 3-dimensional membrane. The resulting Dirac-like equation is then analyzed for general coordinates as well as for the case of a Friedmann-Robertson-Walker metric for spatially closed geometries. The problem of the singularity formation at quantum level is addressed.Comment: 25 pages, 6 figures, v2: extended version, v3: published version, minor correction

    Panel methods: An introduction

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    Panel methods are numerical schemes for solving (the Prandtl-Glauert equation) for linear, inviscid, irrotational flow about aircraft flying at subsonic or supersonic speeds. The tools at the panel-method user's disposal are (1) surface panels of source-doublet-vorticity distributions that can represent nearly arbitrary geometry, and (2) extremely versatile boundary condition capabilities that can frequently be used for creative modeling. Panel-method capabilities and limitations, basic concepts common to all panel-method codes, different choices that were made in the implementation of these concepts into working computer programs, and various modeling techniques involving boundary conditions, jump properties, and trailing wakes are discussed. An approach for extending the method to nonlinear transonic flow is also presented. Three appendices supplement the main test. In appendix 1, additional detail is provided on how the basic concepts are implemented into a specific computer program (PANAIR). In appendix 2, it is shown how to evaluate analytically the fundamental surface integral that arises in the expressions for influence-coefficients, and evaluate its jump property. In appendix 3, a simple example is used to illustrate the so-called finite part of the improper integrals
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