Communications in Mathematical Physics

, Volume 364, Issue 2, pp 607–634 | Cite as

The Motion of Small Bodies in Space-Time

  • Robert Geroch
  • James Owen WeatherallEmail author


We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship between approaches that model such bodies as distributions supported on a curve, and those that employ smooth fields supported in small neighborhoods of a curve. This result also applies to “bodies” constructed from wave packets of Maxwell or Klein–Gordon fields. There follows a simple and precise formulation of the optical limit for Maxwell fields.


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  1. 1.
    Einstein A., Grommer J.: Allgemeine Relativitätstheorie und Bewegungsgesetz. Verlag der Akademie der Wissenschaften, Berlin (1927)zbMATHGoogle Scholar
  2. 2.
    Einstein A., Infeld L., Hoffman B.: The gravitational equations and the problem of motion. Ann. Math. 39(1), 65–100 (1938)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Asada H., Futamase T., Hogan P.A.: Equations of Motion in General Relativity. Oxford University Press, Oxford (2011)zbMATHGoogle Scholar
  4. 4.
    Poisson E., Pound A., Vega I.: The motion of point particles in curved spacetime. In: Living Reviews in Relativity, vol. 14, no. 7 (2011)Google Scholar
  5. 5.
    Gralla S.E., Wald R.M.: A rigorous derivation of gravitational self-force. Class. Quantum Gravity 28(15), 159501 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    Puetzfeld, D., Lämmerzahl, C., Schutz, B. (ed.): Equations of Motion in Relativistic Gravity. Springer, Heidelberg (2011)Google Scholar
  7. 7.
    Malament D.: A remark about the geodesic principle in general relativity. In: Frappier, M., Brown, D.H., DiSalle, R. (eds) Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos, pp. 245–252. Springer, New York (2012)CrossRefGoogle Scholar
  8. 8.
    Dixon W.G.: A covariant multipole formalism for extended test bodies in general relativity. Il Nuovo Cimento 34(2), 317–339 (1964)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Mathisson M.: Die mechanik des materieteilchens in der allgemeinen relativitätstheorie.. Zeitschrift für Physik 67, 826–844 (1931)ADSCrossRefGoogle Scholar
  10. 10.
    Souriau J.-M.: Modèle de particule à spin dans le champ électromagnétique et gravitationnel. Annales de l’Institut Henri Poincaré Sec. A 20, 315 (1974)Google Scholar
  11. 11.
    Sternberg S., Guillemin V.: Symplectic Techniques in Physics. Cambridge University Press, Cambridge (1984)zbMATHGoogle Scholar
  12. 12.
    Geroch R., Jang P.S.: Motion of a body in general relativity. J. Math. Phys. 16(1), 65 (1975)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Ehlers J., Geroch R.: Equation of motion of small bodies in relativity. Ann. Phys. 309, 232–236 (2004)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Papapetrou A.: Spinning test particles in general relativity. Proc. R. Soc. 290, 248–258 (1951)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Weatherall J.O.: The motion of a body in Newtonian theories. J. Math. Phys. 52(3), 032502 (2011)ADSMathSciNetCrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Enrico Fermi InstituteThe University of ChicagoChicagoUSA
  2. 2.Department of Logic and Philosophy of ScienceUniversity of California, IrvineIrvineUSA

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