Titlebook: Ernst Equation and Riemann Surfaces; Analytical and Numer Christian Klein Book 2005 Springer-Verlag Berlin Heidelberg 2005 Einstein equatio

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978-3-642-06677-1Springer-Verlag Berlin Heidelberg 2005

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Ernst Equation and Riemann Surfaces978-3-540-31513-1Series ISSN 0075-8450 Series E-ISSN 1616-6361

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A Three-Step Capital Allocation FrameworkThe solutions to the Ernst equation discussed in the previous chapters are given in terms of multi–dimensional theta functions. Though theta–functional solutions to integrable equations are known since the beginning of the seventies for equations like KdV, the work with these solutions admittedly has not reached the importance of solitons.

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0075-8450 completely integrable Ernst equation. In this volume the solutions to the Ernst equation associated to Riemann surfaces are studied in detail and physical and mathematical aspects of this class are discussed both analytically and numerically. .978-3-642-06677-1978-3-540-31513-1Series ISSN 0075-8450 Series E-ISSN 1616-6361

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https://doi.org/10.1007/3-540-45267-2dimensional Euclidean space characterized by the harmonicity of 1/v-K whereK is the Gaussian curvature. In the case of constant negative Gaussian curvature, this leads e.g. to the pseudo-sphere which is a solution to the integrable sine–Gordon equation. If one studies Bianchi surfaces with non-const

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https://doi.org/10.1007/978-3-658-12025-2e disk. In the Newtonian limit e is approximately 0 whereas it tends to 1 inthe ultrarelativistic limit where the central redshift diverges. The limit of a single component disk is reached for γ = 1 (we will only consider positive values of γ), the staticlimit for γ = 0.

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The Ernst Equation,dimensional Euclidean space characterized by the harmonicity of 1/v-K whereK is the Gaussian curvature. In the case of constant negative Gaussian curvature, this leads e.g. to the pseudo-sphere which is a solution to the integrable sine–Gordon equation. If one studies Bianchi surfaces with non-const