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Arch. Ration. Mech. Anal. 4, 273. Misner, C. , Thorne, K. , and Wheeler, J. A. (1973). Gravitation (Freeman, San Francisco). Wald, R. M. (1984). General Relativity (University of Chicago Press, Chicago). Frenkel, J. (1926). Zeitschr. f. Phys. 37, 243. Weinberg, S. (1972). Gravitation and Cosmology (John Wiley and Sons, New York), p. 47. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. General Relativity and Gravitation, Vol. 33, No. 1, 2001 Null Limits of Generalised Bonnor-Swaminarayan Solutions J.

6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. , and Griffiths, J. B. (1999). Class. Quantum Grav. 16, 2937. Penrose, R. (1972). General Relativity, ed. L. O’Raifeartaigh (Oxford: Clarendon), p. 101. , and Schmidt, B. (1989). Class. Quantum Grav. 6, 1547. , and Schmidt, B. (1989). Phys. Rev. D 40, 1827. Bic˘ a´ k, J. (1985). H. MacCallum, ed. (Cambridge University Press, Cambridge), p. 99. Bic˘ a´ k, J. (1987). In Gravitation and Geometry, W. Rindler and A. Trautman, eds. (Bibliopolis, Naples), p.

To maintain the inequality (3), it is necessary to simultaneously scale the parameter m to zero such that mA remains constant. The parameter J is unchanged by this scaling. However, the parameters Z 1 and Z 2 become zero in these limits, but their ratio remains a finite constant, and all the regularity conditions are thus preserved. Let us first consider the above null limit for the more familiar case B. In this case, we find (expanding to terms in Z 2i ) that the limits of (9) are  a, outside the null cone.

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