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XVII.—The Regraduation of Clocks in Spherically Symmetric Space-times of General Relativity.
Published online by Cambridge University Press: 14 February 2012
Summary
The changes in his description of events brought about by an arbitrary regraduation of an observer's clock are examined, taking the axioms of general relativity as fundamental. It is shown that regraduation does not imply a change from one Riemannian space-time to another but merely a coordinate transformation within space-time. A generalisation of the “dynamical time” of kinematical relativity is a by-product of the investigation.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 62 , Issue 2 , 1946 , pp. 147 - 155
- Copyright
- Copyright © Royal Society of Edinburgh 1946
References
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page 149 note ‡ Purely as a matter of convenience r is measured in the same units as t. To convert to units of length, r must be multiplied by the velocity of light, c.
page 149 note § By evaluating the equations (5) for this space-time, the condition 
must be imposed on g.
page 150 note * The “expanding universes” of general relativity are the special cases of (6) in which 
page 150 note † The angular coordinates θ, Θ, ψ of B do not enter into this discussion.
page 150 note ‡ In kinematical relativity, coordinates t m, r m are used which are the linear combinations t m=½(s 1+s 2), r m=½(s 2–s 1) of s 1, s 2.
page 150 note § We use the index – I throughout to denote an inverse function, not a negative power.
page 152 note * Eisenhart, L. P., Riemannian Geometry, § 28, Princeton Univ. Press, 1926Google Scholar.
page 154 note * In the de Sitter universe 
See, for example, McVittie, G. C., Cosmological Theory, p. 64, Methuen, 1937Google Scholar
.