Past-Future Asymmetry of the Gravitational Field of a Point Particle

Phys. Rev. 110, 965 – Published 15 May 1958
David Finkelstein


The analytic extension of the Schwarzschild exterior solution is given in a closed form valid throughout empty space-time and possessing no irregularities except that at the origin. The gravitational field of a spherical point particle is then seen not to be invariant under time reversal for any admissible choice of time coordinate. The Schwarzschild surface r=2m is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it but only in one direction. The apparent violation of the principle of sufficient reason seems similar to that which is associated with instabilities in other nonlinear phenomena.


  • Received 9 January 1958
  • Published in the issue dated May 1958

© 1958 The American Physical Society

Authors & Affiliations

David Finkelstein

  • Stevens Institute of Technology, Hoboken, New Jersey, and New York University, New York, New York

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