Exact and analytic solutions of the Ernst equation governing axially symmetric stationary vacuum gravitational fields

    Authors

    M. Baxter;R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Phys. Scr.

    Keywords

    HOMOTOPY ANALYSIS METHOD; NONLINEAR DIFFERENTIAL-EQUATIONS; VISCOUS-FLOW; PROBLEMS; NON-NEWTONIAN FLUIDS; EMDEN-FOWLER TYPE; SERIES SOLUTIONS; GENERAL-APPROACH; FORMULATION; WAVES; Physics, Multidisciplinary

    Abstract

    We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions.

    Journal Title

    Physica Scripta

    Volume

    87

    Issue/Number

    3

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    8

    WOS Identifier

    WOS:000315194000006

    ISSN

    0031-8949

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