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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 4, Pages 18–34 (Mi faa323)

Theta Function Solutions of the Schlesinger System and the Ernst Equation

D. A. Korotkina, V. B. Matveevb

a Concordia University, Department of Mathematics and Statistics
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We establish a link between the Schlesinger system and the Ernst equation (the stationary axisymmetric Einstein equation) on the level of algebro-geometric solutions. We calculate all metric coefficients corresponding to general algebro-geometric solutions of the Ernst equation.

DOI: https://doi.org/10.4213/faa323

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English version:
Functional Analysis and Its Applications, 2000, 34:4, 252–264

Bibliographic databases:

UDC: 517.9

Citation: D. A. Korotkin, V. B. Matveev, “Theta Function Solutions of the Schlesinger System and the Ernst Equation”, Funktsional. Anal. i Prilozhen., 34:4 (2000), 18–34; Funct. Anal. Appl., 34:4 (2000), 252–264

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/faa323
• https://doi.org/10.4213/faa323
• http://mi.mathnet.ru/eng/faa/v34/i4/p18

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Frauendiener J., Klein C., “Exact relativistic treatment of stationary counterrotating dust disks: Physical properties”, Physical Review D, 63:8 (2001), 084025
2. Klein C., “Exact relativistic treatment of stationary counterrotating dust disks: Boundary value problems and solutions”, Physical Review D, 63:6 (2001), 064033
3. Klein, C, “Ernst equation, Fay identities and variational formulas on hyperelliptic curves”, Mathematical Research Letters, 9:1 (2002), 27
4. C. Klein, “Isomonodromy Approach to Boundary Value Problems for the Ernst Equation”, Theoret. and Math. Phys., 134:1 (2003), 72–85
5. C. Klein, “The Kerr Solution on Partially Degenerate Hyperelliptic Riemann Surfaces”, Theoret. and Math. Phys., 137:2 (2003), 1520–1526
6. Klein, C, “On explicit solutions to the stationary axisymmetric Einstein-Maxwell equations describing dust disks”, Annalen der Physik, 12:10 (2003), 599
7. Klein, C, “Exact relativistic treatment of stationary black-hole-disk systems”, Physical Review D, 68:2 (2003), 027501
8. Karas, V, “Gravitating discs around black holes”, Classical and Quantum Gravity, 21:7 (2004), R1
9. Katsnelson V., Volok D., “Rational solutions of the Schlesinger system and isoprincipal deformations of rational matrix functions I”, Current Trends in Operator Theory and its Applications, Operator Theory : Advances and Applications, 149, 2004, 291–348
10. Matveev, VB, “30 years of finite-gap integration theory”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 837
11. Lenells J., “Boundary Value Problems for the Stationary Axisymmetric Einstein Equations: A Disk Rotating Around a Black Hole”, Comm Math Phys, 304:3 (2011), 585–635
12. Brezhnev Yu.V., “Spectral/Quadrature Duality: Picard-Vessiot Theory and Finite-Gap Potentials”, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 563, ed. AcostaHumanez P. Finkel F. Kamran N. Olver P., Amer Mathematical Soc, 2012, 1–31
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