, Volume 18, Issue 3, pp 131–135 | Cite as

Conformal Killing tensors of order 2 for the Schwarzschild metric

  • Giacomo Caviglia


A base for the real vector space identified by the trace-free conformal Killing tensors admitted by the Schwarzschild metric is explicitly exhibited. In particular it follows that this vector space is ten dimensional and consists only of degenerate conformal Killing tensors.


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Si determina esplicitamente una base per lo spazio vettoriale reale formato dai tensori di Killing conformi di ordine due a traccia nulla ammessi dalla metrica di Schwarzschild. In particolare si prova che tale spazio vettoriale ha dimensione dieci e che contiene soltanto tensori di Killing di tipo ridondante.


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  1. [1]
    Walker M., andPenrose R.,On Quadratic First Integrals of the Geodesic Equations for Type {2, 2} Spacetimes, Commun. Math. Phys., vol. 18, 1970, pp. 265–274.Google Scholar
  2. [2]
    Caviglia G., Salmistraro F., andZordan C.,Geodesic Deviation and First Integrals of Motion, J. Math. Phys., in print.Google Scholar
  3. [3]
    Benenti S. andFrancaviglia M.,The theory of Separability of the Hamilton-Jacobi Equation and Its Applications to General Relativity, inGeneral Relativity and Gravitation I, Held A. edit., Plenum, New York, 1980.Google Scholar
  4. [4]
    Havas P.,Separation of Variables in the Hamilton-Jacobi, Schrödinger, and Related Equations, II. Partial Separation, J. Math. Phys., vol. 16, 1975, pp. 2476–2489.Google Scholar
  5. [5]
    Zordan C., Salmistraro F., andCaviglia G.,On a Classification of Conformal Killing Tensors, N. Cim B, in print.Google Scholar
  6. [6]
    Weir G.J.,Conformal Killing Tensors in Reducible Spaces, J. Math. Phys., vol. 18, 1977, pp. 1782–1787.Google Scholar
  7. [7]
    Hughston L.P., Penrose R., Sommers P., Walker M.,On a Quadratic First Integral for the Charged Particle Orbits in the Charged Kerr Solution, Commun. Math., Phys., vol. 27, 1972, pp. 303–308.Google Scholar
  8. [8]
    Hughston L.P. andSommers P.,Spacetime with Killing Tensors, Commun. Math. Phys., vol. 32, 1973, pp. 147–152.Google Scholar
  9. [9]
    Newman E. andPenrose R.,An Approach to Gravitational Radiation by a Method of Spin Coefficients, J. Math. Phys., vol. 3, 1962, pp. 566–578.Google Scholar
  10. [10]
    Ikeda M. andKimura M.,On Quadratic First Integrals in the General Relativistic Kepler Problem, Tensor, vol. 25, 1972, pp. 395–404.Google Scholar
  11. [11]
    Caviglia G. andZordan C.,Third Order Killing Tensors in the Schwarzschild Spacetime, Gen. Rel. Grav., vol. 14, 1982, pp. 27–30.Google Scholar
  12. [12]
    Godfrey B.B.,Horizon in Weyl Metrics Exhibiting Extra Symmetries, Gen. Rel. Grav., vol. 3, 1972, pp. 3–16.Google Scholar
  13. [13]
    Mc Intosh C.B.G.,Homothetic Motions in General Relativity, Gen. Rel. Grav., vol. 7, 1976, pp. 199–213.Google Scholar
  14. [14]
    Campbell S.J. andWainwright J.,Algebraic Computing and the Newman-Penrose Formalism in General Relativity, Gen. Rel. Grav., vol. 8, 1977, pp. 987–1001.Google Scholar
  15. [15]
    Kinnersley W.,Type D Vacuum Metrics, J. Math. Phys., vol. 10, 1969, pp. 1195–1203.Google Scholar
  16. [16]
    Chandrasekhar S.,An Introduction to the Theory of the Kerr Metric and Its Perturbations, inGeneral Relativity, Hawking S.W. and Israel W. edits., Cambridge University Press, Cambridge, 1979.Google Scholar

Copyright information

© Pitagora Editrice Bologna 1983

Authors and Affiliations

  • Giacomo Caviglia
    • 1
  1. 1.Istituto Matematico dell'UniversitàGenovaItaly

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