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Past-Future Asymmetry of the Gravitational Field of a Point Particle
Abstract
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.
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Citations
Cited by
Theory and Experiment in Gravitational Physics
Will, C. M. (2018) · doi:10.1017/9781316338612 · Cited by 3,637
Gravitational Collapse and Space-Time Singularities
Penrose, R. (1965) · Physical Review Letters · doi:10.1103/physrevlett.14.57 · Cited by 2,977
The 1965 Penrose singularity theorem
Senovilla, J. M. M., & Garfinkle, D. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/12/124008 · Cited by 248
Conserved charges in general relativity
Aoki, S., Onogi, T., & Yokoyama, S. (2021) · International Journal of Modern Physics A · doi:10.1142/s0217751x21500986 · Cited by 34
Analytic models for gravitational collapse
Aoki, S., & Ovalle, J. (2025) · Physical Review D · doi:10.1103/physrevd.111.024037 · Cited by 7
Metadata
- Authors
- Finkelstein, D.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1958-05-15
- Volume
- 110
- Issue
- 4
- Pages
- 965-967
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2034066066
- Cited by
- 537
- References
- 0
- FWCI
- 11.17
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
