Abstract
A method is given for investigating the ultrarelativistic encounter of two black holes which complements the usual low-speed approximation. It depends on the fact that the ultrarelativistic limit of a moving Schwarzschild black hole is a certain plane-fronted impulsive gravitational wave. This enables linearized theory on a curved background to be used. The solution is obtained, with the help of generalized function techniques, to the first order in the background energy, and the radiation pattern at conformal null infinity is examined. The whole approach has a strong connection with the theory of twistors.
Similar content being viewed by others
References
D'Eath, P. D. (1975).Phys. Rev. D,12, 2183–2199.
D'Eath, P. D. (1978).Phys. Rev. D, (in press).
Matzner, R. A., and Nutku, Y. (1974).Proc. Roy. Soc. A336, 285–305.
Smarr, L. (1975).The Structure of General Relativity with a Numerical Illustration: The Collison of Two Black Holes. Ph.D. Thesis, University of Texas at Austin.
Curtis, G. E. (1975).Twistor Theory and the Collision of Plane-Fronted Impulsive Gravitational Waves. D. Phil. Thesis, Oxford University.
Aichelburg, P. C., and Sexl, R. U. (1971):Gen. Rel Grav.,2, 303–312.
Curtis, G. E. (1978).Gen. Rel Grav.,9, 987–997.
Gel'fand, I. M., and Shilov, G. E. (1964).Generalized Functions (Academic Press, New York), vol. 1.
Newman, E. T., and Penrose, R. (1968).Proc. Roy. Soc. A,336, 285–305.
Penrose, R., and MacCallum, M. A. H. (1973).Phys. Rep.,6C, 243–315.
Penrose, R. (1968). InBattelle Rencontres, edited by C. M. DeWitt and J. A. Wheeler (Benjamin, New York).
Penrose, R. (1972). InGeneral Relativity, Papers in Honour of J. L. Synge, edited by L. O'Raifeartaigh. (Clarendon Press, Oxford).
Kahn, K. A., and Penrose, R. (1971).Nature,229, 185–186.
Szekeres, P. (1972).J. Math. Phys.,13, 286–294.
Bondi, H., van der Burg, M. G. J., and Metzner, A. W. K. (1962).Proc. Roy. Soc. A,269, 21–52.
Pirani, F. A. E. (1959).Proc. Roy. Soc. A,252, 96–101.
Penrose, R. (1975). InQuantum Gravity, edited by C. J. Isham, R. Penrose, and D. W. Sciama, (University Press, Oxford).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Curtis, G.E. Ultrarelativistic black-hole encounters. Gen Relat Gravit 9, 999–1008 (1978). https://doi.org/10.1007/BF00784660
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00784660