On the attractive force of the gravitational field in static space times
- 1 July 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 68 (1) , 187-197
- https://doi.org/10.1017/s0305004100001225
Abstract
A static metric is considered. A meaningful definition of gravitational force is given and the potential, which is the norm of the Killing vector ξa, is studied. For the case that the metric is asymptotically flat, the following is shown: The equi-potential surfaces are closed 2-dimensional surfacesSlying in the rest space V3, which is the hypersurface orthogonal to ξa. All the surfacesSenclose matter, and the gravitational force points intoStowards the enclosed matter. A test particle starting atSwill be pulled into the domain bounded bySand will never leave this domain.This publication has 4 references indexed in Scilit:
- On the analyticity of static vacuum solutions of Einstein's equationsMathematical Proceedings of the Cambridge Philosophical Society, 1970
- Elementary Differential Topology. (AM-54)Published by Walter de Gruyter GmbH ,1963
- Morse Theory. (AM-51)Published by Walter de Gruyter GmbH ,1963
- The Behavior of a Function on Its Critical SetAnnals of Mathematics, 1939