Skip to main content
SpringerLink
Log in

References

  • Chapter
  • First Online:
Ernst Equation and Riemann Surfaces

Part of the book series: Lecture Notes in Physics ((LNP,volume 685))

  • 763 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E.D. Belokolos, A.I. Bobenko, V.Z. Enolskii, A.R. Its, V.B. Matveev: Algebro-geometric approach to nonlinear integrable equations, (Springer, Berlin 1994)

    MATH  Google Scholar 

  2. M. Audin: Spinning tops, (Cambridge University Press, Cambridge 1996)

    MATH  Google Scholar 

  3. S.V. Kovalevski: Acta Math. 12, 177 (1889)

    MathSciNet  Google Scholar 

  4. S.A. Chaplygin: Collected works Vol. 1, (Gostekhizdat, Moscow 1948)

    Google Scholar 

  5. V.I. Arnold: Mathematical methods of classical mechanics, (Springer, Berlin 1978)

    MATH  Google Scholar 

  6. W. Thirring: Lehrbuch der mathematischen Physik Bd. 1 (Springer, Wien 1977)

    MATH  Google Scholar 

  7. R. Abraham, J.E. Marsden: Foundations of mechanics (Addison–Wesley, Reading 1978)

    MATH  Google Scholar 

  8. A.M. Perelomov: Integrable systems of classical mechanics and Lie algebras Vol. 1, (Birkhäuser, Basel 1990)

    Google Scholar 

  9. C.S. Gardner, J.M. Greene, M.D. Kruskal, R.M. Miura: Phys. Rev. Lett 10, 1095 (1967)

    ADS  Google Scholar 

  10. D.J. Korteweg, G. de Vries: Phil. Mag. 39, 422 (1895)

    Google Scholar 

  11. M. Toda: Nonlinear waves and solitons, (Kluwer, Dordrecht 1989)

    MATH  Google Scholar 

  12. P.G. Drazin, R.S. Johnson: Solitons: an introduction (Cambridge University Press, Cambridge 1989)

    MATH  Google Scholar 

  13. P.D. Lax: Comm. Pure Appl. Math. 21, 467 (1968)

    MATH  MathSciNet  Google Scholar 

  14. L.D. Faddeev, L.A. Takhtajan: Hamiltonian Methods in the Theory of Solitons, (Springer, Berlin 1987)

    MATH  Google Scholar 

  15. A.C. Newell: Solitons in Mathematics and Physics, CBMS 48, (SIAM, Philadelphia 1986)

    Google Scholar 

  16. F. Calogero, A. Degasperis: Spectral Transforms and Solitons, Studies in Mathematics and its Applications 13, (North-Holland, Amsterdam-New York 1982)

    Google Scholar 

  17. M. Ablowitz, H. Segur: Solitons and the inverse scattering transform, SIAM Studies in Applied Mathematics 4, (SIAM, Philadelphia 1981)

    Google Scholar 

  18. R. Penrose: Twistors as spin 3/2 charges. In Gravitation and modern cosmology, ed by A. Zichchi, N. Sánchez (Plenum Press, New York).

    Google Scholar 

  19. F.B. Estabrook, H.D. Wahlquist: J. Math. Phys. 16, 1 (1975); J. Math. Phys. 17, 1 (1976)

    ADS  MATH  MathSciNet  Google Scholar 

  20. M.J. Ablowitz, A. Ramani, H. Segur: Lett. Nuovo Cim. 23, 333 (1978)

    MathSciNet  Google Scholar 

  21. M.J. Ablowitz, A. Ramani, H. Segur: J. Math. Phys. 21, 715 (1980); J. Math. Phys. 21, 1006 (1980)

    ADS  MATH  MathSciNet  Google Scholar 

  22. J.B. McLeod and P.J. Olver, SIAM J. Math. Anal. 14, 488 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Weiss, M. Tabor, G. Carnevale: J. Math. Phys. 24, 522 (1983)

    ADS  MathSciNet  MATH  Google Scholar 

  24. V.E. Zakaharov: What is integrability?, (Springer, Berlin 1991)

    Google Scholar 

  25. A.S. Fokas, U. Mugan, M.J. Ablowitz: Physica D 30, 247 (1988)

    Article  ADS  MathSciNet  ISI  MATH  Google Scholar 

  26. F. Nijhoff, N. Joshi, A. Hone: Phys. Lett. A 267, 147 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. M. Gürses: Lett. Math. Phys. 11, 59 (1986)

    MATH  MathSciNet  ADS  Google Scholar 

  28. R.S. Ward: Phil. Trans. R. Soc. Lond. A 315, 451 (1985)

    ADS  MATH  Google Scholar 

  29. K.K. Uhlenbeck: Commun. Math. Phys. 83, 11 (1982)

    MATH  MathSciNet  ADS  Google Scholar 

  30. R.S. Ward, R.O. Wells Jr.: Twistor geometry and field theory, (Cambridge University Press, Cambridge 1995)

    Google Scholar 

  31. M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, Yu.I. Manin: Phys. Lett. A65, 185 (1978)

    ADS  MathSciNet  Google Scholar 

  32. L.J. Mason, N.M.J. Woodhouse: Integrability, self-duality and twistor theory, (Clarendon Press, Oxford 1996)

    MATH  Google Scholar 

  33. N.J. Hitchin: Introduction. In Integrable systems–twistors, loop groups, and Riemann surfaces, ed by N.M.J. Woodhouse, (Clarendon Press, Oxford 1999), pp 1

    Google Scholar 

  34. F.J. Ernst: Phys. Rev 167, 1175 (1968)

    Article  ADS  Google Scholar 

  35. H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt: Exact solutions of Einstein's field equations, 2nd edn (Cambridge: Cambridge University Press 2003)

    MATH  Google Scholar 

  36. V.A. Belinski, E. Verdaguer: Gravitational Solitons, (Cambridge, Cambridge University Press 2001)

    MATH  Google Scholar 

  37. P. Forgács, Z. Horváth, L. Palla: Phys. Rev. Lett. 45, 505 (1980)

    ADS  MathSciNet  Google Scholar 

  38. P. Forgács, Z. Horváth, L. Palla: Phys. Rev. D 23 1876 (1981)

    ADS  MathSciNet  Google Scholar 

  39. P. Forgács, Z. Horváth, L. Palla: Phys. Lett. B 99 232 (1981).

    ADS  MathSciNet  Google Scholar 

  40. P. Forgács, Z. Horváth, L. Palla: Ann. Phys. 136 371 (1981)

    ADS  Google Scholar 

  41. P. Forgács, Z. Horváth, L. Palla: Nucl. Phys. B 192 141 (1981)

    ADS  Google Scholar 

  42. C.N. Yang: Phys. Rev. Lett. 38, 1377 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  43. S. Weinberg: Phys. Rev. 166, 1568 (1968)

    Article  ADS  Google Scholar 

  44. K. Meetz: J. Math. Phys. 10, 65 (1969)

    Article  MathSciNet  Google Scholar 

  45. S. Coleman, J. Wess, B. Zumino: Phys. Rev. 177, 2239 (1968)

    ADS  Google Scholar 

  46. S. Ketov: Quantum Nonlinear Sigma–Models (Springer, Berlin 2000)

    MATH  Google Scholar 

  47. W.J. Zakrzewski: Low-dimensional Sigma Models (Adam Hilger, Bristol 1989)

    MATH  Google Scholar 

  48. H. Eichenherr, M. Forger: Nucl. Phys. B, 155, 381 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  49. J. Eells, Jr., J.H. Sampson: Amer. J. Math., 86, 109 (1964)

    MathSciNet  MATH  Google Scholar 

  50. L. Bianchi: Lezioni di Geometria Differenziale, (Pisa 1909)

    Google Scholar 

  51. D. Korotkin: J. Math. Sciences, 94 1177 (1999)

    MathSciNet  Google Scholar 

  52. D.A. Korotkin: Theor. Math. Phys. 77, 1018 (1989)

    MathSciNet  Google Scholar 

  53. S. Novikov, S.V. Manakov, L.P. Pitaevskii, V.E. Zakharov: Theory of solitons: the inverse scattering method, (Consultants Bureau, New York 1984)

    Google Scholar 

  54. I.M. Gel'fand, B.M. Levitan: Izv. Akad. Nauk SSSR Ser. Mat. 15, 309 (1951); A.M.S. Transl. (2) 1, 253

    Google Scholar 

  55. V.A. Marchenko: Dokl. Akad. Nauk SSSR 104, 695 (1955) (in Russian)

    MATH  MathSciNet  Google Scholar 

  56. A.R. Its, V. Matveev: Theor. Math. Phys. 23, 51 (1975)

    Article  MathSciNet  Google Scholar 

  57. A.R. Its, V. Matveev: Funct. Anal. Appl. 9, 69 (1975)

    Article  MathSciNet  Google Scholar 

  58. V. Matveev: 30 years of finite-gap integration theory. In 30 Years of Finite Gap Integration, ed by V. Kusnetsov, to appear in Phil. Trans. London Math. Soc., (2005)

    Google Scholar 

  59. G. B. Whitham: SIAM J. of App. Math. 14, 956 (1966)

    MATH  MathSciNet  Google Scholar 

  60. G. B. Whitham: Linear and Nonlinear Waves, (Wiley, New York/London/ Sidney 1999)

    MATH  Google Scholar 

  61. A. G. Gurevich, L. P. Pitaevskii: Sov. Phys. JETP 38 (2), 909 (1992)

    MathSciNet  Google Scholar 

  62. P. Lax, D. Levermore: Commun. Pure Appl. Math. 36, 253, 571, 809 (1983)

    MATH  MathSciNet  Google Scholar 

  63. S. Venakides: Commun. Pure Appl. Math. 38, 125 (1983)

    MathSciNet  Google Scholar 

  64. R. Geroch: J. Math. Phys. 12, 918 (1971)

    MATH  MathSciNet  ADS  Google Scholar 

  65. A. Einstein, N. Rosen: J. Franklin Inst. 223, 43 (1937)

    ADS  Google Scholar 

  66. H. Weyl: Ann. Physik 54, 117 (1917)

    MATH  ADS  Google Scholar 

  67. R.P. Kerr: Phys. Rev. Lett. 11, 237 (1963)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  68. K.A. Khan, R. Penrose: Nature 229, 185 (1971)

    Article  ISI  ADS  Google Scholar 

  69. R.A. Matzner, C.W. Misner: Phys. Rev. 154, 1229 (1967)

    Article  ADS  Google Scholar 

  70. G. Weinstein: Comm. Pure Appl. Math. 43, 903 (1990)

    MATH  MathSciNet  Google Scholar 

  71. G. Weinstein: Comm. Pure Appl. Math. 45, 1183 (1992)

    MATH  MathSciNet  Google Scholar 

  72. G. Weinstein: Duke Math. J. 77, 1183 (1995)

    Article  MathSciNet  Google Scholar 

  73. G. Weinstein: Amer. J. Math. 118, 689 (1996)

    MATH  MathSciNet  Google Scholar 

  74. M. Mars, J.M. Senovilla: Modern Phys. Lett. A 13, 1509 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  75. D. Maison: Phys. Rev. Lett. 41, 521 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  76. D. Maison, J. Math. Phys. 20, 871 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  77. V.A. Belinski, V.E. Zakharov: Sov. Phys.–JETP 48, 985 (1978)

    ADS  Google Scholar 

  78. P. Breitenlohner, D. Maison: Ann. Inst. H. Poincaré 46 215, (1987)

    MathSciNet  MATH  Google Scholar 

  79. D. Korotkin: J. Phys. A 26, 3823 (1993)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  80. C.M. Cosgrove: J. Math. Phys. 21, 2417 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  81. R. Geroch: J. Math. Phys. 13, 394 (1972)

    MATH  MathSciNet  ADS  Google Scholar 

  82. I. Hauser, F.J. Ernst: J. Math. Phys. 22, 1051 (1981)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  83. I. Hauser, F.J. Ernst: gr-qc/0002049 (2000)

    Google Scholar 

  84. B. Julia: Infinite dimensional algebras in physics. In: Johns Hopkins workshop on current problems in particle physics: unified field theories and beyond, (Johns Hopkins University, Baltimore 1981)

    Google Scholar 

  85. P. Breitenlohner, D. Maison: Explicit and Hidden Symmetries of Dimensionally Reduced (Super)Gravity Theories. In Solutions to Einstein's Equations: Techniques and Results, ed by C. Hoenselaers, W. Dietz, Lecture Notes in Physics 205, (Springer, Berlin 1983) pp 276

    Google Scholar 

  86. B. Julia: In Superspace and Supergravity, ed. by S. Hawking, M. Roček, (Cambridge University Press, Cambridge 1981)

    Google Scholar 

  87. H. Nicolai: Two-dimensional gravities and supergravities as integrable systems. In Recent aspects of quantum fields, ed by H. Mitter, H. Gausterer, (Springer, Berlin 1991)

    Google Scholar 

  88. N.M.J. Woodhouse, L.J. Mason: Nonlinearity 1, 73 (1988)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  89. R.S. Ward: Comm. Math. Phys. 79, 317 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  90. D. Korotkin, V. Matveev: Leningrad Math. J. 1, 379 (1990)

    MathSciNet  MATH  Google Scholar 

  91. D.A. Korotkin: Commun. Math. Phys. 137 383 (1991)

    MATH  MathSciNet  ADS  Google Scholar 

  92. D.A. Korotkin: Class. Quant. Grav. 8 L219 (1991)

    ADS  MathSciNet  Google Scholar 

  93. D.A. Korotkin: Class. Quant. Grav. 10 2587 (1993)

    ADS  MATH  MathSciNet  Google Scholar 

  94. D. Korotkin, V. Matveev: Lett. Math. Phys. 49, 145 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  95. D.A. Korotkin, V.B. Matveev: Funct. Anal. Appl. 34, 18 (2000)

    Article  MathSciNet  Google Scholar 

  96. M. Babich, D.A. Korotkin: Lett. Math. Phys. 46, 323 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  97. J.B. Hartle, D.H. Sharp: Astrophys. J. 147, 317 (1967)

    Article  ADS  Google Scholar 

  98. L. Lindblom: Astrophys. J. 208, 873 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  99. R. Schödel et al.: Nature 419, 694 (2002)

    ADS  Google Scholar 

  100. U. Heilig: Ann. Inst. Henri Poincaré, Physique Théorique 60 457 (1994)

    MATH  MathSciNet  Google Scholar 

  101. U. Heilig: Comm. Math. Phys. 166 457 (1995)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  102. H.D. Wahlquist: Phys. Rev. 172 1291 (1968)

    Article  ADS  Google Scholar 

  103. D. Kramer: Class. Quant. Grav. 1, L3 (1984)

    ADS  Google Scholar 

  104. J.M. Senovilla: Phys. Lett. 123A, 211 (1987)

    ADS  MathSciNet  Google Scholar 

  105. M. Bradley, G. Fodor, M. Marklund, Z. Perjés: Class. Quant. Grav. 17, 351 (2000)

    ADS  MATH  Google Scholar 

  106. J. Binney, S. Tremaine: Galactic Dynamics, (Princeton University Press, Princeton 1987)

    MATH  Google Scholar 

  107. U.M. Schaudt, H. Pfister: Phys. Rev. Lett. 77, 3284 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  108. U.M. Schaudt: Commun. Math. Phys. 190, 509 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  109. G. Neugebauer, R. Meinel: Astrophys. J. 414, L97 (1993)

    ADS  Google Scholar 

  110. G. Neugebauer, R. Meinel: Phys. Rev. Lett. 73, 2166 (1994)

    Article  ADS  Google Scholar 

  111. G. Neugebauer, R. Meinel: Phys. Rev. Lett. 75, 3046 (1995)

    ADS  MathSciNet  MATH  Google Scholar 

  112. C. Klein, O. Richter: Phys. Rev. D 57, 857 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  113. C. Klein: Phys. Rev. D63, 064033 (2001)

    ADS  Google Scholar 

  114. C. Struck: Phys. Rep. 321, 1 (1999)

    Article  ADS  Google Scholar 

  115. V.C. Rubin, J.A. Graham, J.D.P. Kenney: Astrophys. J. 394, L9 (1992)

    Article  ADS  Google Scholar 

  116. H.-W. Rix, M. Franx, D. Fisher, G. Illingworth: Astrophys. J 400, L5 (1992)

    Article  ADS  Google Scholar 

  117. J. Bičák, T. Ledvinka: Phys. Rev. Lett. 71, 1669 (1993)

    ADS  MathSciNet  MATH  Google Scholar 

  118. C. Klein, O. Richter: Phys. Rev. Lett. 79, 565 (1997)

    ADS  Google Scholar 

  119. J. Frauendiener, C. Klein: Phys. Rev. D 63, 084023 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  120. D. Maison: Duality and Hidden Symmetries in Gravitational Theories. In Einstein's Field equations and Physical Implications, Lecture Notes Phys. 540 ed by B.G. Schmidt (Springer, Berlin 2000) pp 1

    Google Scholar 

  121. J. Ehlers: Konstruktion und Charakterisierungen von Lösungen der Einstein'schen Gravitationsgleichungen, PHD thesis, Universität Hamburg, Hamburg (1957)

    Google Scholar 

  122. H. Röhrl: Math. Ann. 151, 365 (1963)

    MathSciNet  Google Scholar 

  123. C. Klein, O. Richter: J. Geom. Phys. 30, 331 (1999)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  124. I.M. Krichever: Itogi nauki i techniki, Current problems in mathematics, 23, 79 (VINITI, Moscow 1983) (in Russian)

    Google Scholar 

  125. R. Meinel, G. Neugebauer: Phys. Lett. A 210, 160 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  126. D.A. Korotkin: Phys. Lett. A 229 195 (1997)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  127. C. Klein, D. Korotkin, V. Shramchenko: Math. Res. Lett. 9, 27 (2002)

    MathSciNet  MATH  Google Scholar 

  128. J.D. Fay: Theta functions on Riemann surfaces, Lecture Notes on Mathematics 352, (Springer, New York 1973)

    Google Scholar 

  129. C. Klein, O. Richter: Phys. Rev. D58, CID 124018 (1998)

    Google Scholar 

  130. C. Klein, O. Richter: Phys. Rev. Lett. 83, 2884 (1999)

    Article  ADS  Google Scholar 

  131. J. Frauendiener, C. Klein: J. Comp. Appl. Math. 167, 193 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  132. www.lorene.obspm.fr

    Google Scholar 

  133. C. Klein: Theor. Math. Phys. 137, 1520 (2003)

    Article  MATH  Google Scholar 

  134. C. Klein: Phys. Rev. D 68, 027501 (2003)

    ADS  MathSciNet  Google Scholar 

  135. W. Kinnersley: J. Math. Phys. 18, 1529 (1977)

    ADS  Google Scholar 

  136. B. Harrison: J. Math. Phys. 9, 1744 (1968)

    Article  MATH  ADS  Google Scholar 

  137. C. Klein: Phys. Rev. D 65, 084029 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  138. H.M. Farkas, I. Kra: Riemann surfaces, Graduate Texts in Mathematics, Vol. 71, (Berlin, Springer 1993).

    Google Scholar 

  139. D. Mumford: Tata lectures on Theta Vol. Vol. II, Progress in Mathematics, Vol. 43, (Birkhäuser, Boston 1993)

    Google Scholar 

  140. S.W. Hawking, G.F.R. Ellis: The large scale structure of space–time, (Cambridge University Press, Cambridge 1973)

    MATH  Google Scholar 

  141. N.S. Manton: Nucl. Phys. B 135, 319 (1978)

    Article  ADS  Google Scholar 

  142. V.A. Belinski, V.E. Zakharov: Sov. Phys.–JETP 50, 1 (1979)

    ADS  Google Scholar 

  143. P. Houston, L.O. O'Raifeartaigh: Phys. Lett. B 93 151 (1980)

    ADS  MathSciNet  Google Scholar 

  144. S. Weinberg: Gravitation and cosmology, (John Wiley & Sons, New York 1972)

    Google Scholar 

  145. C.W. Misner, K.S. Thorne, J.A. Wheeler: Gravitation, (Freeman, New York 1973)

    Google Scholar 

  146. R.M. Wald: General relativity, (The University of Chicago Press, Chicago 1984)

    MATH  Google Scholar 

  147. H. Stephani: Relativity, 2nd edn (Cambridge University Press, Cambridge 2004)

    Google Scholar 

  148. J.L. Synge: Relativity: the general theory, (North-Holland Publishing Company, Amsterdam 1960)

    MATH  Google Scholar 

  149. W. Thirring: Lehrbuch der mathematischen Physik Vol. 2, (Springer, Wien 1978)

    Google Scholar 

  150. H. Weyl: Raum – Zeit – Materie, (Springer, Berlin 1923)

    Google Scholar 

  151. W. Pauli: Theory of relativity, (Dover, New York 1981)

    Google Scholar 

  152. F. de Felice, C.J.S. Clarke: Relativity on curved manifolds, (Cambridge University Press, Cambridge 1990)

    MATH  Google Scholar 

  153. J. Stewart: Advanced general relativity, (Cambridge University Press, Cambridge 1990)

    MATH  Google Scholar 

  154. T. Lewis: Proc. Roy. Soc. London A 136, 176 (1932)

    ADS  MATH  Google Scholar 

  155. A. Papapetrou: Ann. Inst. H. Poincaré A 4, 83 (1966)

    Google Scholar 

  156. G. Neugebauer: J. Phys. A 12, L67 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  157. P. Fordy, J.C. Wood: Aspects Math. 23 (1993)

    Google Scholar 

  158. M.F. Atiyah: The geometry of Yang–Mills fields, (Lezione Fermiane, Scuola Normale Superiore Pisa 1979)

    Google Scholar 

  159. L. Bianchi: Ann. Math. 18, 301 (1890)

    MATH  Google Scholar 

  160. S. Finikov: Theorie der Kongruenzen, (Akademie–Verlag 1959)

    Google Scholar 

  161. A. Bobenko: Aspects Mat. 23 (1993)

    Google Scholar 

  162. D. Korotkin, V. Reznik: Math. Notes 52, 930 (1992)

    Article  MathSciNet  Google Scholar 

  163. J. Fletcher, N.M.J. Woodhouse: Twistor characterization of stationary axisymmetric solutions of Einstein's equations. In Twistors in mathematics and physics, ed by T.N. Bailey, R.J. Baston, (Cambridge University Press, Cambridge, 1990) pp 260

    Google Scholar 

  164. T. von Schroeter: Twistor classification of type D vacuum space–times, In Twistor Newsletter.

    Google Scholar 

  165. J. Fletcher: More on the twistor description of the Kerr solution. In: Twistor Newsletter.

    Google Scholar 

  166. S. Kolditz: Zur Twistorformulierung einer speziellen Klasse von Lösungen der Ernst–Gleichung, diploma thesis, University of Leipzig (2002)

    Google Scholar 

  167. L. Witten: Phys. Rev. D19, 718 (1979)

    ADS  Google Scholar 

  168. R.S. Ward: Gen. Rel. Grav. 15, 105 (1983)

    Article  ADS  MATH  Google Scholar 

  169. G. 't Hooft: Nucl. Phys. B 79, 276 (1974)

    ADS  MathSciNet  Google Scholar 

  170. A.M. Polyakov: JETP Lett. 20, 194 (1974)

    ADS  Google Scholar 

  171. M.K. Prasad, C.M. Sommerfield: Phys. Rev. Lett. 35, 760 (1975)

    Article  ADS  Google Scholar 

  172. E.B. Bogomolny: Sov. J. Nucl. Phys. 24, 861 (1976)

    Google Scholar 

  173. H.M. Farkas: Journ. d'Anal. Math. 44, 205 (1984–85)

    MathSciNet  Google Scholar 

  174. H.M. Farkas: Contem. Math. 136, 161 (1992)

    MATH  MathSciNet  Google Scholar 

  175. H.M. Farkas: Israel Math. Conference Proc. 9, 231 (1996)

    MATH  MathSciNet  Google Scholar 

  176. C. Poor: Proc. of the AMS 114, 667 (1992)

    MATH  MathSciNet  Google Scholar 

  177. A. Bobenko, L. Bordag: J. Phys. A 22, 1259 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  178. J. Frauendiener, C. Klein: to appear in Lett. Math. Phys. (2005).

    Google Scholar 

  179. H.E. Rauch: Comm. Pure Appl. Math. 12, 543 (1959)

    MathSciNet  Google Scholar 

  180. S.I. Zverovich: Russ. Math. Surv. (Uspekhi) 26, 117 (1971)

    ADS  Google Scholar 

  181. Yu.L. Rodin: The Riemann boundary problem on Riemann surfaces, (Reidel, Dordrecht 1988)

    MATH  Google Scholar 

  182. N.I. Muskhelishvili: Singular Integral Equations, (Noordhoff, Groningen 1953)

    MATH  Google Scholar 

  183. G. Neugebauer: In General Relativity, ed by G.S. Hall, J.R. Pulham, (SUSSP Publication, Edinburgh, and IOP, London 1996), pp 61

    Google Scholar 

  184. C. Klein, O. Richter: J. Geom. Phys. 24, 53 (1997)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  185. H. Grauert: Math. Ann. 135, 263 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  186. B.A. Dubrovin: Russ. Math. Surv. (Uspekhi) 36, 11 (1981)

    MATH  MathSciNet  ADS  Google Scholar 

  187. H. Stahl: Theorie der Abel'schen Funktionen, (Teubner, Leipzig 1896)

    Google Scholar 

  188. P.A. Griffiths: Bull. Amer. Math. Soc. 76, 228 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  189. D.R. Morrison: Picard–Fuchs equations and mirror maps for hypersurfaces. In Essays on mirror manifolds, ed by S.-T. Yau, (Hong Kong: International Press, 1992)

    Google Scholar 

  190. F. Foucault: C. R. Acad. Sci. 314, Série I, 617 (1992)

    MATH  MathSciNet  Google Scholar 

  191. Yu.I. Manin: Izv. Akad. Nauk S.S.S.R. Ser. Mat. 22, 737 (1958); A.M.S. Transl. (2) 37, 59

    MATH  MathSciNet  Google Scholar 

  192. B.B. Kadomtsev, V. Petviashvili: Dokl. Akad. Nauk 192, 753 (1970)

    Google Scholar 

  193. I.M. Krichever: Funct. Anal. Appl. 9, 84 (1975)

    Article  Google Scholar 

  194. B.A. Dubrovin, R. Flickinger, H. Segur: Stud. Appli. Math., 99(2), 137 (1997)

    MathSciNet  Google Scholar 

  195. M. Jimbo, T. Miwa, K. Ueno: Physica D 2, 306 (1981)

    ADS  MathSciNet  ISI  MATH  Google Scholar 

  196. A. Yamada: Kodai Math. Journ. 3, 114 (1980)

    MATH  Google Scholar 

  197. H. Müller zum Hagen: Proc. Camb. Phil. Soc. 68, 199 (1970)

    MATH  Google Scholar 

  198. C.B. Morrey: Am. J. Math. 80, 198 (1958)

    MATH  MathSciNet  Google Scholar 

  199. H. Bateman, A. Erdélyi: Higher transcendental functions, (McGraw–Hill, New York 1955)

    MATH  Google Scholar 

  200. A. Tomimatsu, H. Sato: Phys. Rev. Lett. 29, 1344 (1972)

    Article  ADS  Google Scholar 

  201. A. Tomimatsu, H. Sato: Prog. Theor. Phys. 50, 95 (1973)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  202. C. Hoenselaers, W. Kinnersley, B.C. Xanthopoulos: J. Math. Phys. 20, 2530 (1979)

    ADS  Google Scholar 

  203. D. Korotkin, H. Nicolai: Nucl. Phys. B 475, 397 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  204. T. Morgan, L. Morgan: Phys. Rev. 183, 1097 (1969); Errata: 188, 2544 (1969)

    Article  ADS  Google Scholar 

  205. J.M. Bardeen, R.V. Wagoner: Astrophys. J. 167, 359 (1971)

    ADS  MathSciNet  Google Scholar 

  206. J. Bičák, D. Lynden-Bell, J. Katz: Phys. Rev. D, 47, 4334 (1993)

    ADS  MathSciNet  Google Scholar 

  207. J. Bičák, D. Lynden-Bell, C. Pichon: MNRAS 256, 126 (1993)

    ADS  Google Scholar 

  208. C. Pichon, D. Lynden-Bell: MNRAS 280, 1007 (1996)

    ADS  Google Scholar 

  209. W. Israel: Nuovo Cimento 44 B, 4349 (1966); Errata: 48 2583 (1966); 44B 1 (1966); 48B, 463 (1967)

    Google Scholar 

  210. M. Ansorg, R. Meinel: Gen. Relativ. Gravit. 32, 1365 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  211. R. Geroch: J. Math. Phys. 11, 2580 (1970)

    MathSciNet  MATH  ADS  Google Scholar 

  212. R. Hansen: J. Math. Phys. 15, 46 (1974)

    Article  MATH  ADS  Google Scholar 

  213. G. Fodor, C. Hoenselaers, Z. Perjés: J. Math. Phys. 30, 2252 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  214. I. Hauser, F. Ernst: J. Math. Phys. 21, 1126 (1980)

    ADS  MathSciNet  Google Scholar 

  215. P. Kordas: Class. Quantum Grav. 12, 2037, (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  216. R. Meinel, G. Neugebauer: Class. Quantum Grav. 12, 2045, (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  217. C. Klein: Theor. Math. Phys. 134, 72 (2003)

    Article  MATH  Google Scholar 

  218. K. Thorne: Nonspherical Gravitational Collapse: A Short Review. In Magic Without Magic: John Archibald Wheeler, ed by J. Klauder (W. H. Freeman: San Francisco 1972) pp 231

    Google Scholar 

  219. C.L. Tretkoff, M.D. Tretkoff: Contemp. Math. 33, 467 (1984)

    MathSciNet  Google Scholar 

  220. M. Seppälä: Discrete Comput. Geom. 11, 65 (1994)

    MATH  MathSciNet  Google Scholar 

  221. M. Hoeij: J. Symb. Comput. 18, 353 (1994)

    MATH  Google Scholar 

  222. P. Gianni, M. Seppälä, R. Silhol, B. Trager: J. Symb. Comp. 26, 789 (1998)

    MATH  Google Scholar 

  223. B. Deconinck, M. van Hoeij, Physica D 152–153, 28 (2001)

    MathSciNet  Google Scholar 

  224. B. Deconinck, M. Heil, A. Bobenko, M. van Hoeij, M. Schmies: Math. Comp. 73, 1417 (2004)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  225. www-sfb288.math.tu-berlin.de/ jtem/

    Google Scholar 

  226. V.Z. Enolski, P.H. Richter: Periods of hyperelliptic integrals expressed in terms of theta-constants by means of Thomae formulae. In 30 Years of Finite Gap Integration, ed by V. Kusnetsov, to appear in Phil. Trans. London Math. Soc., (2005)

    Google Scholar 

  227. A. Komar: Phys. Rev. 113, 934 (1959)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  228. E. Gourgoulhon, S. Bonazzola: Class. Quant. Grav. 11, 443 (1994)

    ADS  MathSciNet  Google Scholar 

  229. B. Fornberg: A practical guide to pseudospectral methods, (Cambridge University Press, Cambridge 1996)

    MATH  Google Scholar 

  230. W. L. Briggs, V. E. Henson: The DFT, an owner's manual for the discrete Fourier transform, (Siam, Philadelphia 1995)

    MATH  Google Scholar 

  231. M. Heil: Numerical Tools for the study of finite gap solutions of integrable systems, PhD thesis, TU Berlin, Berlin (1995)

    Google Scholar 

  232. E. Gourgoulhon, P. Haensel, R. Livine, E. Paluch, S. Bonazzola, J.-A. Marck: Astr. Astrophys. 349 851 (1999)

    ADS  Google Scholar 

  233. C. Klein, Theor. Math. Phys. 127, 767 (2001)

    Article  MATH  Google Scholar 

  234. R. Meinel: The rigidly rotating disk of dust and its black hole limit. In Recent Developments in Gravitation and Mathematical Physics, ed by A. Garcí a, C. Lämmerzahl, A. Mací as, T. Matos, D. Nuñes, (Science Network Publishing: Konstanz 1998), gr-qc/9703077

    Google Scholar 

  235. M. Rees: In Black Holes and Relativistic Stars, ed by R. Wald (Univ. Chicago Press, Chicago 1998) pp 79

    Google Scholar 

  236. A. Laor: Phys, Rep. 311, 451 (1999)

    Article  ADS  Google Scholar 

  237. S. Chakrabarti (ed.): Observational Evidence for the Black holes in the Universe (Kluwer, Dordrecht 1999)

    Google Scholar 

  238. C. DeWitt, B. DeWitt (ed.): Black holes, (Gordon and Breach, New York 1973)

    Google Scholar 

  239. O. Semerák: Towards gravitating disks around rotating black holes. In Gravitation: Following the Prague Inspiration, ed by O. Semerák, J. Podolský, M. Žofka, (World Scientific, Singapore 2002), pp 111

    Google Scholar 

  240. V. Karas, J.-M. Huré, O. Semerák: Class. Quant. Grav. 21, R1 (2004)

    ADS  MATH  Google Scholar 

  241. B. Carter: Black hole equilibrium states. In Black holes, ed by C. DeWitt and B. S. DeWitt, (Gordon & Breach, New York 1973)

    Google Scholar 

  242. C. Klein: Ann. Phys. (Leipzig) 12, 599 (2003)

    ADS  MATH  Google Scholar 

  243. C. Klein: Class. Quantum Grav. 14, 2267 (1997)

    Article  ADS  MATH  Google Scholar 

  244. J. Lemos, P. Letelier: Phys. Rev. D 49, 5135 (1994)

    ADS  Google Scholar 

  245. F.J. Ernst: Phys. Rev 168, 1415 (1968)

    Article  ADS  Google Scholar 

  246. D. Maison: In Developments in the Theory of Fundamental Interaction, ed by L. Turko, A. Pekalski,

    Google Scholar 

  247. G. Weinstein, Comm. Part. Diff. Equ. 21, 1389 (1996)

    MATH  MathSciNet  Google Scholar 

  248. D. Maison: Stationary Solutions of the Einstein-Maxwell Equations. In Nonlinear equations in classical and quantum field theory (Meudon/Paris, 1983/1984), Lecture Notes in Phys.

    Google Scholar 

  249. M. King, H. Pfister: Phys. Rev. D 65, 084033 (2002)

    ADS  Google Scholar 

  250. M. King, H. Pfister: Class. Quant. Grav. 20, 205 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  251. J. Novak, E. Marcq: Class. Quant. Grav. 20, 3051 (2003) 226, (Springer, Berlin 1985) pp 125

    ADS  MATH  MathSciNet  Google Scholar 

  252. G. Neugebauer, D. Kramer: J. Phys. A 16, 1937 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  253. D. Korotkin: Math. Ann. 329 335 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  254. A. Kitaev, D. Korotkin: Int. Math. Res. Not. 17, 877 (1998)

    MathSciNet  Google Scholar 

  255. A. Kokotov, D. Korotkin: math-ph/0310008 (2003)

    Google Scholar 

  256. G. Springer: Introduction to Riemann surfaces, (Addison–Wesley, Reading 1957)

    MATH  Google Scholar 

  257. L. Alfors, L. Sario: Riemann surfaces, (Princeton University Press, N.J. 1960)

    Google Scholar 

  258. M. Atiyah: Riemann Surfaces and spin structures, (Annales Scientifiques de l'Ecole Normale Supérieure, 1971).

    Google Scholar 

  259. A.F. Beardon: A Primer on Riemann Surfaces, London Mathematical Society Lecture Notes 78, (Cambridge University Press, Cambridge 1984)

    Google Scholar 

  260. J.-B. Bost: Introduction to Compact Riemann Surfaces, Jacobians and Abelian Varieties. In From Number theory to Physics, ed by M. Waldschmidt, P. Moussa, J.-M. Kuck, C. Itzykson, (Springer, Berlin 1992)

    Google Scholar 

  261. J. Jost: Compact Riemann Surfaces, (Springer, Berlin 19997)

    Google Scholar 

  262. J. Lewittes: Acta Math. 111, 35 (1964)

    MathSciNet  Google Scholar 

  263. A. Hurwitz, R. Courant: Funktionentheorie, (Springer, Berlin 1964)

    MATH  Google Scholar 

  264. P. Griffiths, J. Harris: Principles of algebraic geometry, (John Wiley & Sons, New York 1978)

    MATH  Google Scholar 

  265. S.S. Chern: Complex manifolds without potential theory, (Springer, New York 1995)

    MATH  Google Scholar 

  266. R.C. Gunning: Lectures on Riemann surfaces, (Princeton University Press, Princeton 1967)

    MATH  Google Scholar 

  267. A. Krazer, W. Wirtinger: Abelsche Funktionen und allgemeine Thetafunktionen. In Encyklopädie der mathematischen Wissenschaften II (2), Heft 7, (Teubner, Leipzig 1915)

    Google Scholar 

  268. A.I. Markushevich: Introduction to the classical theory of Abelian functions, (American Mathematical Society, Providence 1992).

    MATH  Google Scholar 

  269. M. Koecher, A. Krieg: Elliptische Funktionen und Modulformen, (Springer, Berlin 1998)

    MATH  Google Scholar 

  270. A. Krazer: Lehrbuch der Thetafunktionen, (Teubner, Leipzig 1903)

    MATH  Google Scholar 

  271. O. Richter, C. Klein: Algebro-geometric approach to the Ernst equation I. In Mathematics of Gravitation, Banach Center Publications 41, ed by P.T. Chruściel, (PAS, Inst. Math., Warsaw 1997) pp 195

    Google Scholar 

  272. I.A. Taimanov: Russian Math. Surveys 52, 147 (1997)

    MATH  MathSciNet  ADS  Google Scholar 

  273. S. Kobayashi, K. Nomizu: Foundations of differential geometry Vol. I, (Plenum, New York 1963)

    MATH  Google Scholar 

  274. M.F. Atiyah: The geometry of Yang–Mills fields, Lezione Fermiane, Scuola Normale Superiore Pisa (1979)

    Google Scholar 

  275. M.F. Atiyah, N.J. Hitchin, I.M. Singer, Proc. R. Soc. Lond. A 362, 425 (1978)

    ADS  MathSciNet  MATH  Google Scholar 

  276. H. Baum: Self-dual connections and holomorphic bundles. In Self-dual Riemannian Geometry and Instantons, ed by T. Friedrich, (Teubner, Leipzig 1981) pp 105

    Google Scholar 

  277. N.J. Hitchin: Riemann surfaces and integrable systems. In Integrable systems–twistors, loop groups, and Riemann surfaces 1, ed by N.M.J. Woodhouse, (Clarendon Press, Oxford 1999)

    Google Scholar 

  278. G. Dell'Antonio, S. Doplicher, Jona-Lasinio: Mathematical Problems in Theoretical Physics Lecture Notes in Physics, 80, (Springer, Berlin et al. 1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany

    Christian Klein

Authors
  1. Christian Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this chapter

Cite this chapter

Klein, C. References. In: Ernst Equation and Riemann Surfaces. Lecture Notes in Physics, vol 685. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11540953_9

Download citation

  • DOI: https://doi.org/10.1007/11540953_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28589-2

  • Online ISBN: 978-3-540-31513-1

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation