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Note on Relativistic Mechanics

Published online by Cambridge University Press:  20 January 2009

A. G. Walker
A. G. Walker
Affiliation:
University of Oxford.
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The object of this note is to derive a form of Poisson's equation from general relativistic mechanics, without assuming the field to be either static or “weak”. The problem is essentially a “local” problem, all observations being made by one observer; this observer determines the apparent gravitational field in his vicinity by observing the motions of free (isolated) particles. Defining gravitational mass by means of Poisson's equation, we find the relation between the densities of gravitational and inertial mass relative to any observer. We also find what may be called the non-rotating frame of reference belonging to any observer.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 3 , August 1935 , pp. 170 - 174
Copyright
Copyright © Edinburgh Mathematical Society 1935

References

page 170 note 1 The line element of V 4 has the significance that the element of distance in an instantaneous space is the element of length measured by a rigid scale, and the element of distance along a world-line is the element of proper-time multiplied by the velocity of light.

page 171 note 1 See Walker, A. G., “Relative Coordinates,” Proc. Boy. Soc. Edinburgh, 52 (1932), 346.Google Scholar

page 171 note 2 Eddington, The Mathematical Theory of Relativity (1930), § 56.Google Scholar

page 172 note 1 Walker, loc. cit. p. 351. The right-hand side of (4.3) should read – v r instead of v r; we are now writing gσ for vσ. It must be remembered that in the V 4 we are considering, the indicators areGoogle Scholar

page 172 note 2 CfWhittaker, E. T.Proc. Roy. Soc., 149 A (1935), 385.CrossRefGoogle Scholar

page 173 note 1 Whittaker, E. T.loc. cit.Google Scholar; and Ruse, H. S., page 151 (5.7) of the present volume of Proc. Edin. Math. Soc.Google Scholar

page 173 note 2 Eddington, op. cit., §53.Google Scholar