Skip to main content
SpringerLink
Log in

Schwarzschild Radius Before General Relativity: Why Does Michell-Laplace Argument Provide the Correct Answer?

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

A famous Newtonian argument by Michell and Laplace, regarding the existence of “dark bodies” and dating back to the end of the 18th century, is able to provide an exact general-relativistic result, namely the exact formula for the Schwarzschild radius. Since general relativity was formulated more than a century after this argument had been issued, it looks quite surprising that such a correct prediction could have been possible. Far from being merely a fortuitous coincidence (as one might justifiably be induced to think), this fact can find a reasonable explanation once the question is approached the other way round, i.e. from the general-relativistic point of view. By reexamining Laplace’s proof from this point of view, we discuss here the reasons why Michell-Laplace argument can be so “unexpectedly" correct in its general-relativistic prediction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Michell, J.: On the means of discovering the distance, magnitude, &c. of the fixed stars, in consequence of the diminution of the velocity of their light, in case such a diminution should be found to take place in any of them, and such other data should be procured from observations, as would be farther necessary for that purpose, by the Rev. John Michell, B.D.F.R.S. In a letter to Henry Cavendish, Esq. F.R.S. and A.S. Phil. Trans. R. Soc. Lond. 74, 35–57 (1784). Read November 27, 1783

    Article  Google Scholar 

  2. Laplace, P.-S.: Exposition du Système du Monde, tome 2. Imprimerie du Cercle-Social, Paris (1796), p. 305

    Google Scholar 

  3. Wheeler, J.A.: Our universe: the known and the unknown. Public lecture held at the Goddard Institute of Space Studies on December 29, 1967. Am. Sch. 37, 248–274 (1968)

    Google Scholar 

  4. Wheeler, J.A.: Our universe: the known and the unknown. Public lecture held at the Goddard Institute of Space Studies on December 29, 1967, continued. Am. Sci. 56, 1–20 (1968)

    ADS  Google Scholar 

  5. Oppenheimer, J.R., Snyder, H.: On continued gravitational contraction. Phys. Rev. 56, 455–459 (1939)

    Article  MATH  ADS  Google Scholar 

  6. Laplace, P.-S.: Beweis des Satzes, daß die anzihende Kraft bey einem Weltkörper so groß seyn könne, daß das Licht davon nicht ausströmen kann. Allgemeine Geographische Ephemeriden. Verfasset von einer Gesellshaft Gelehrten und herausgegeben von F. von Zach, H.S.G. Obristwachtmeister und Director der herzoglichen Sternwarte Seeberg bey Gotha. Vierter Band. Weimar, Im Verlage des Industrie-Comptoirs 1799, pp. 1–6. An English translation of this paper can be found, e.g., in: Hawking, S.W., Ellis, G.F.R., The Large Scale Structure of Space-time, Cambridge University Press, Cambridge (1973), Appendix A

  7. McVittie, G.C.: Laplace’s alleged ‘black hole’. The Observatory 98, 272–274 (1978)

    ADS  Google Scholar 

  8. Sheldon, E.: A champion to the rescue of Laplace. The Observatory 99, 91–93 (1979)

    ADS  Google Scholar 

  9. Eisenstaedt, J.: Dark body and black hole horizons. Gen. Relativ. Gravit. 23, 75–80 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  10. Glendenning, N.K.: Special and General Relativity. Springer, New York (2007), p. 176: “It is not clear to this autho[r] why classical reasoning should have lead to an exact result of General Relativity.”

    MATH  Google Scholar 

  11. Eisenstaedt, J.: Avant Einstein: Relativité, Lumière, Gravitation. Seuil, Paris (2005)

    Google Scholar 

  12. Eisenstaedt, J.: From Newton to Einstein: a forgotten relativistic optics of moving bodies. Am. J. Phys. 75, 741–746 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  13. Bradley, J.: A letter from the Reverend Mr. James Bradley Savilian Professor of Astronomy at Oxford, and F.R.S. to Dr. Edmund Halley, Astronom. Reg. &c. giving an account of a new discovered motion of the fix’d stars. Phil. Trans. R. Soc. Lond. 35, 637–661 (1728)

    Google Scholar 

  14. Römer, O.: Demonstration touchant le mouvement de la lumiere trouvè par M. Römer de l’Academie Royale des Sciences. J. Scavans 233–236 (1676)

  15. Römer, O.: A demonstration concerning the motion of light, communicated from Paris, in the Journal des Scavans, and here made English. Phil. Trans. R. Soc. Lond. 136, 893–894 (1677)

    Google Scholar 

  16. von Soldner, J.G.: Ueber die ablenkung eines lichtstrals von seiner geradlinigen bewegung. durch die Attraktion eines Weltkörpers, an welchem er nahe vorbei geht. Berliner Astronomisches Jahrbuch, s. 161–172 (1801). At regard, see also [11,12]

  17. Jaki, S.L.: Johann Georg von Soldner and the gravitational bending of light, with an English translation of his essay on it published in 1801. Found. Phys. 8, 927–950 (1978)

    Article  ADS  Google Scholar 

  18. de Felice, F., Preti, G.: A generalized principle of relativity. Chaos, Solitons Fractals (2008, in press). doi:10.1016/j.chaos.2008.04.041

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica “Galileo Galilei”, Università degli Studi di Padova, and INFN, Sezione di Padova, Padova, Italy

    Giovanni Preti

Authors
  1. Giovanni Preti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giovanni Preti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Preti, G. Schwarzschild Radius Before General Relativity: Why Does Michell-Laplace Argument Provide the Correct Answer?. Found Phys 39, 1046–1054 (2009). https://doi.org/10.1007/s10701-009-9315-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-009-9315-8

Keywords

Search

Navigation