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Everywhere invariant spaces of metrics and isometries

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Abstract

We define an everywhere invariant space of metricsU to be one for which the set of diffeomorphisms, which leaveU invariant, contains all the isometries of the individual metrics inU. We also generalize Killing's equation to a new equation, the invariance equation, which has as solutions those vector fields which leaveU invariant. By combining these ideas we give a new method for finding the isometries of a given metric.

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References

  1. Kinnersley, W. (1974). Paper presented at the Seventh International conference on General Relativity, Tel-Aviv, Israel.

  2. d'Inverno, R. A. and Smallwood, J. (1978).Gen. Rel. Grav.,9, 195–214.

    Google Scholar 

  3. d'Inverno, R. A. and Smallwood, J. (1978).Gen. Rel. Grav.,9, 215–225.

    Google Scholar 

  4. Omori, J. (1968).Proc. Symp. Pure Maths. XV, 167–184.

    Google Scholar 

  5. Schwartz, J. T. (1969).Nonlinear Functional Analysis (Gordon and Breach, New York).

    Google Scholar 

  6. Ebin, P. G. (1968).Proc. Symp. Pure Maths.,XV, 11–40.

    Google Scholar 

  7. Palais, R. S. (1960).Ann. Math.,73, 295–323.

    Google Scholar 

  8. Isenberg, J. and Marsden, J. (1982).Phys. Rep.,89, 179–222.

    Google Scholar 

  9. Kramer, D., Stephani, H., MacCallum, M., Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).

    Google Scholar 

  10. Swift, S. T., d'Inverno, R. A., Vickers J. A. G. (1984).Functional Form Invariance in General Relativity and Geometry, University of Southampton Preprint.

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Authors and Affiliations

  1. Department of Mathematics, University of Southampton, S09 5NH, Southampton, England

    S. T. Swift, R. A. d'Inverno & J. A. G. Vickers

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  1. S. T. Swift
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  2. R. A. d'Inverno
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  3. J. A. G. Vickers
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Swift, S.T., d'Inverno, R.A. & Vickers, J.A.G. Everywhere invariant spaces of metrics and isometries. Gen Relat Gravit 18, 1093–1103 (1986). https://doi.org/10.1007/BF00763536

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  • DOI: https://doi.org/10.1007/BF00763536

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