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Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein’s Equations

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Abstract

This paper contains an investigation of spaces with a two parameter Abelian isometry group in which the Hamilton-Jacobi equation for the geodesies is soluble by separation of variables in such a way that a certain natural canonical orthonormal tetrad is determined. The spaces satisfying the stronger condition that the corresponding Schrodinger equation is separable are isolated in a canonical form for which Einstein’s vacuum equations and the source-free Einstein-Maxwell equations (with or without a Λ term) can be solved explicitly. A fairly extensive family of new solutions is obtained including the previously known solutions of de Sitter, Kasner, Taub-NUT, and Kerr as special cases.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, Cambridge, UK

    Brandon Carter

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  1. Brandon Carter
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Carter, B. Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein’s Equations. Commun.Math. Phys. 10, 280–310 (1968). https://doi.org/10.1007/BF03399503

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  • DOI: https://doi.org/10.1007/BF03399503

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