General Relativity and Gravitation

, Volume 20, Issue 6, pp 607–622 | Cite as

An exact solution of Einstein's equations for two particles falling freely in an external gravitational field

  • W. B. Bonnor
Research Articles


I begin with a Weyl axially symmetric, static metric representing a spherical particle in equilibrium under the attraction of a semi-infinite rod (s.i.r.) of line density 1/2 and another, pseudo-uniform, gravitational field. A coordinate transformation is then used to remove the s.i.r., enlarge the spacetime, and make the solution time-dependent. The result represents two spherical particles (which do not interact because each is outside the null cone of the other) moving in a certain gravitational wave field. It is shown that the particles move on geodesies of the background wave field. The sources of the wave field are briefly investigated.


Exact Solution Spherical Particle Differential Geometry Gravitational Field Coordinate Transformation 
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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • W. B. Bonnor
    • 1
  1. 1.Department of Mathematics and Applied MathematicsThe University of NatalDurbanSouth Africa

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