Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-30T00:18:51.339Z Has data issue: false hasContentIssue false

On the extendibility of Weyl coordinates

Published online by Cambridge University Press:  24 October 2008

H. Müller Zum Hagen
Affiliation:
King's Collage, London

Extract

Axially symmetric static fields produced by one extended body are considered. The metric outside the body is the Weyl metric which can be written in so-called Weyl coordinates in the form ds2 = a2(dr2 + dz2) + b2dϕ2c2dt2 (a, b, c functions of (r, z) and r > 0) with b2 = r2c−2. Criteria are found under which these Weyl coordinates can be extended through the whole of the body so that ds2 keeps the form above (although in general b2 ǂ r2c−2 inside the body). In the spherically symmetric (⇒ axially symmetric) case it is shown that the Weyl coordinates cover the whole of spacetime only if one allows r < 0 in a certain part of the body.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1) Bondi–Pirani–Trautman. Brandeis lectures: lectures on general relativity (Prentice Hall, Inc. Englewood Cliffs; New Jersey, 1964).Google Scholar
(2)Synge, J. L.Relativity: the general theory (North-Holland Publishing Company; Amsterdam, 1964).Google Scholar
(3)Courant, R. and Hilbert, D.Methods of mathematical physics, volume ii (Interscience Publishers; New York, London, Sydney, 1966).Google Scholar
(4)Ehlers, J. and Kundt, W. Exact solutions of the gravitational field equations. Published in: Gravitation: an introduction to current research. Editor: Witten, L. W. (Wiley; New York, 1962).Google Scholar
(5)Yano, K. and Bochner, S.Curvature and Betti numbers (Princeton University Press; New Jersey, 1953).Google Scholar