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

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Funktsional'nyi Analiz i ego Prilozheniya, 2000, Volume 34, Issue 4, Pages 18–34
DOI: https://doi.org/10.4213/faa323 (Mi faa323)

This article is cited in 18 scientific papers (total in 18 papers)

Theta Function Solutions of the Schlesinger System and the Ernst Equation

D. A. Korotkin^a, V. B. Matveev^b

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

Full-text PDF (229 kB) Citations (18)

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

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.

Received: 26.04.1999

English version:
Functional Analysis and Its Applications, 2000, Volume 34, Issue 4, Pages 252–264
DOI: https://doi.org/10.1023/A:1004153222818

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/faa323

https://doi.org/10.4213/faa323

https://www.mathnet.ru/eng/faa/v34/i4/p18

This publication is cited in the following 18 articles:

Korotkin D., “Bergman Tau-Function: From Einstein Equations and Dubrovin-Frobenius Manifolds to Geometry of Moduli Spaces”, Integrable Systems and Algebraic Geometry: a Celebration of Emma Previato'S 65Th Birthday, Vol 2, London Mathematical Society Lecture Note Series, 459, eds. Donagi R., Shaska T., Cambridge Univ Press, 2020, 215–287
Lenells J., Pei L., “Exact Solution of a Neumann Boundary Value Problem For the Stationary Axisymmetric Einstein Equations”, J. Nonlinear Sci., 29:4 (2019), 1621–1657
Mathew Baxter, Robert A Van Gorder, “Exact and analytic solutions of the Ernst equation governing axially symmetric stationary vacuum gravitational fields”, Phys. Scr., 87:3 (2013), 035005
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
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
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
A. Doliwa, M. Nieszporski, P. M. Santini, “Integrable lattices and their sublattices. II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices”, Journal of Mathematical Physics, 48:11 (2007)
Christian Klein, Lecture Notes in Physics, 685, Ernst Equation and Riemann Surfaces, 2005, 237
Karas, V, “Gravitating discs around black holes”, Classical and Quantum Gravity, 21:7 (2004), R1
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
C. Klein, “Isomonodromy Approach to Boundary Value Problems for the Ernst Equation”, Theoret. and Math. Phys., 134:1 (2003), 72–85
C. Klein, “The Kerr Solution on Partially Degenerate Hyperelliptic Riemann Surfaces”, Theoret. and Math. Phys., 137:2 (2003), 1520–1526
Klein, C, “On explicit solutions to the stationary axisymmetric Einstein-Maxwell equations describing dust disks”, Annalen der Physik, 12:10 (2003), 599
Klein, C, “Exact relativistic treatment of stationary black-hole-disk systems”, Physical Review D, 68:2 (2003), 027501
C. Klein, “On explicit solutions to the stationary axisymmetric Einstein‐Maxwell equations describing dust disks”, Annalen der Physik, 515:10 (2003), 599
Klein, C, “Ernst equation, Fay identities and variational formulas on hyperelliptic curves”, Mathematical Research Letters, 9:1 (2002), 27
Frauendiener J., Klein C., “Exact relativistic treatment of stationary counterrotating dust disks: Physical properties”, Physical Review D, 63:8 (2001), 084025
Klein C., “Exact relativistic treatment of stationary counterrotating dust disks: Boundary value problems and solutions”, Physical Review D, 63:6 (2001), 064033

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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