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Uniqueness of the Newman–Janis Algorithm in Generating the Kerr–Newman Metric

Abstract

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be “derived” by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr–Newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman–Janis algorithm works, many physicist considering it to be an ad hoc procedure or “fluke” and not worthy of further investigation. Contrary to this belief this paper shows why the Newman–Janis algorithm is successful in obtaining the Kerr–Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman–Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein–Maxwell equations is the Kerr–Newman metric.

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REFERENCES

  1. 1.

    Newman, E. T., and Janis, A. I. (1965). J. Math. Phys. 6, 915.

    Google Scholar 

  2. 2.

    Newman, E. T., Couch, E., Chinnapared, K., Exton, A., Prakash, A., and Torrence, R. (1965). J. Math. Phys. 6, 918.

    Google Scholar 

  3. 3.

    Flaherty, E. J. (1976). Hermitian and K¨ahlerian Geometry in Relativity (Lecture notes in Physics 46, Springer-Verlag, Berlin).

    Google Scholar 

  4. 4.

    Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973). Gravitation (W. H. Freeman, San Francisco).

    Google Scholar 

  5. 5.

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

    Google Scholar 

  6. 6.

    Drake, S. P., and Turolla, R. (1997). Class. QuantumGr av. 14, 1883.

    Google Scholar 

  7. 7.

    Newman, E. T., and Penrose, R. (1962). J. Math. Phys. 3, 566.

    Google Scholar 

  8. 8.

    Talbot, C. J. (1965). Commun. Math. Phys. 13, 45.

    Google Scholar 

  9. 9.

    Hawking, S. W., and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge).

    Google Scholar 

  10. 10.

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

    Google Scholar 

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Drake, S.P., Szekeres, P. Uniqueness of the Newman–Janis Algorithm in Generating the Kerr–Newman Metric. General Relativity and Gravitation 32, 445–457 (2000). https://doi.org/10.1023/A:1001920232180

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Keywords

  • Black Hole
  • Field Equation
  • Differential Geometry
  • Maxwell Equation
  • Perfect Fluid