Gauss' Theorem in a General Space-time
- 1 August 1935
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 4 (3) , 144-158
- https://doi.org/10.1017/s0013091500008142
Abstract
In classical mechanics Gauss' Theorem for a gravitational field states that, if S is a closed surface and N the component of gravitational force along the outward normal, thenwhere β is the Newtonian constant of gravitation and M is the total mass inside S. This result has recently been extended to general relativity by E. T. Whittaker,1 who, however, considered only the case of a statical gravitational field, the line-element of which is given by2where the coefficients U and αμν are independent of t. It is not immediately clear from his work whether the results are extensible to more general space-times.Keywords
This publication has 1 reference indexed in Scilit:
- On Gauss' theorem and the concept of mass in general relativityProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1935