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Integrability Versus Separability for the Multi-Centre Metrics

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Abstract

The multi-centre metrics are a family of euclidean solutions of the empty space Einstein equations with self-dual curvature. For this full class, we determine which metrics do exhibit an extra conserved quantity quadratic in the momenta, induced by a Killing-Stäckel tensor. Our systematic approach brings to light a subclass of metrics which correspond to new classically integrable dynamical systems. Within this subclass we analyze on the one hand the separation of coordinates in the Hamilton-Jacobi equation and on the other hand the construction of some new Killing-Yano tensors.

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References

  1. Aliev, A.N., Hortacsu, M., Kalayci, J., Nutku, Y.: Class. Quant. Grav. 16, 189–210 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Belinskii, V.A., Gibbons, G.W., Page, D.N., Pope, C.N.: Phys. Lett. B 76, 433–435 (1978)

    Article  Google Scholar 

  3. Boyer, C.P., Finley, J.D.: J. Math. Phys. 23, 1126–1130 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  4. Eguchi, T., Hanson, A.J.: Phys. Lett. B 74, 249–251 (1978)

    Article  Google Scholar 

  5. Feher, L.G., Horváthy, P.A.: Phys. Lett. B 183, 182–186 (1987)

    Article  MathSciNet  Google Scholar 

  6. Gegenberg, J.D., Das, A.: Gen. Rel. Grav. 16, 817–829 (1984)

    MathSciNet  MATH  Google Scholar 

  7. Gibbons, G., Hawking, S.: Phys. Lett. B 78, 430–432 (1978)

    Article  Google Scholar 

  8. Gibbons, G.W., Manton, N.S.: Nucl. Phys. B 274, 183–224 (1986)

    Article  MathSciNet  Google Scholar 

  9. Gibbons, G.W., Olivier, D., Ruback, P.J., Valent, G.: Nucl. Phys. B 296, 679–696 (1988)

    Article  MathSciNet  Google Scholar 

  10. Gibbons, G.W., Ruback, P.J.: Commun. Math. Phys. 115, 267–300 (1988)

    MathSciNet  MATH  Google Scholar 

  11. Hitchin, N.: Math. Proc. Camb. Phil. Soc. 85, 465–476 (1979)

    MathSciNet  MATH  Google Scholar 

  12. Hitchin, N.: Monopoles, minimal surfaces and algebraic curves. In: NATO Advanced Study Institute n° 105, Montreal, Canada: Presses Université de Montreal, 1987

  13. Katzin, H., Levine, J.: Tensor 16, 97 (1965)

    Google Scholar 

  14. Kloster, S., Som, M., Das, A.: J. Math. Phys. 15, 1096–1102 (1974)

    Google Scholar 

  15. Mignemi, S.: J. Math. Phys. 32, 3047–3054 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  16. Perelomov, A.M.: Integrable systems of classical mechanics and Lie algebras. Basel-Boston-Berlin: Birkhäuser Verlag, 1990

  17. Tod, K.P., Ward, R.S.: Proc. Roy. Soc. London A 368, 411–427 (1979)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et des Hautes Energies, Unité associée au CNRS UMR 7589, 2 Place Jussieu, 75251, Paris Cedex 05, France

    Galliano Valent

  2. CNRS Luminy Case 907, Centre de Physique Théorique, 13288, Marseille Cedex 9, France

    Galliano Valent

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  1. Galliano Valent
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Communicated by H. Nicolai

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Valent, G. Integrability Versus Separability for the Multi-Centre Metrics. Commun. Math. Phys. 244, 571–594 (2004). https://doi.org/10.1007/s00220-003-1002-6

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  • DOI: https://doi.org/10.1007/s00220-003-1002-6

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