On the extendibility of Weyl coordinates
Published online by Cambridge University Press: 24 October 2008
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) + b2dϕ2 – c2dt2 (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
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 1 , July 1969 , pp. 155 - 161
- Copyright
- Copyright © Cambridge Philosophical Society 1969
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