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An acceleration condition for b-incomplete timelike curves

Published online by Cambridge University Press:  24 October 2008

C. T. J. Dodson ,
L. J. Sulley  and
P. M. Williams
C. T. J. Dodson
Affiliation:
University of Lancester
L. J. Sulley
Affiliation:
University of Lancester
P. M. Williams
Affiliation:
University of Lancester
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Abstract

The b-completion of a smooth manifold with linear connection was introduced by Schmidt (6). He pointed out that, in a spacetime, an inextensible timelike curve of finite proper length and bounded acceleration has an endpoint on the b-boundary. However, it is not clear in what sense boundedness was meant. Geroch(1) suggested that any acceptable method of completing a spacetime should have this property with boundedness interpreted through the Lorentz norm. This result for the b-completion was given by Rosso(4), based on his earlier paper (3), which, however, contains some arguments that we do not accept. We give another proof of the result and improve it by weakening the condition of boundedness of the acceleration.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 191 - 193
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

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