General Relativity today

  • Thibault Damour
Part of the Progress in Mathematical Physics book series (PMP, volume 52)


After recalling the coceptual foundations and the vasic sturcture of general relativity, we review some of its main modern developments (apart from cosmology): ( i ) the post-Newtonian limit and weak-field tests in the solar system, (ii) strong gravitationl feelds and black holes, (iii) strong-field and radiative tests in binary pulsar observations, (iv) gravitational waves, (v) general relativity and quantum theory.


Black Hole String Theory Neutron Star Gravitational Wave Open String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Einstein, Zur Elektrodynamik bewegter Körper, Annalen der Physik 17 (1905), 891.ADSGoogle Scholar
  2. [2]
    See for an entry into the Einstein Collected Papers Project. The French reader will have access to Einstein’s main papers in Albert Einstein, (Euvres choisies, Paris, Le Seuil/CNRS, 1993, under the direction of F. Balibar. See in particular Volumes 2 (Relativités I) and 3 (Relativités II). One can also consult the 2005 Poincaré seminar dedicated to Einstein (rs URL ): Einstein, 1905-2005, Poincaré Sem- (Birkhäuser Verlag, Basel, Suisse, 2006). See also the excellent summary article by D. Giulini and N. Straumann, “Einstein’s impact on the physics of the twentieth century,” Studies in History and Philosophy of Modern Physics 37 (2006), 115-173. For online access to many of Einstein’s original articles and to documents about him, particular the archive gr-qc. Review articles on certain sub-fields of general relativUpon Einstein, A K Peters Ltd, Wellesley, 2006, for a recent non-technical account of the formation of Einstein’s ideas.
  3. [3]
    GALILEO, Dialogues Concerning Two New Sciences, translated by Henry Crew and Alfonso di Salvio, Macmillan, New York, 1914.Google Scholar
  4. [4]
    The reader inteested in learning about recent experimental tests or gravitational theories may consult, on the internet, either the highly detailed review by C.M. Will in Living Reviews ( or the brief review by T. Damour in the Review of Particle Physics ( See also John Mester’s contribution to this Poincaré seminar.
  5. [5]
    A. Einstein, Die Feldgleichungen der Gravitation, Sitz, Preuss. Ákad. Wiss., 1915, p. 844.Google Scholar
  6. [6]
    The reader wishing to study the formalism and applications of general relativity in detail can consult, for example, the following works: L. Landau and E. Lifshitz, The Classical Theory of Fields, Butterworth-Heinemann, 1995; S. Weinberg, Gravitation and Cosmology, Wiley, New York, 1972; H.C. Ohanian and R Ruffini, Gravitation and Spacetime, Second Edition, Norton, New York, 1994; N. Straumann, General CNRS, Paris, 2002.Google Scholar
  7. [7]
    B. Bertotti, L. Iess, and P. Tortora, A Test of General Relativity using Radio Links with the Cossini Spacecraft, Nature 425 (2003), 374.CrossRefADSGoogle Scholar
  8. [8]
  9. [9]
    W. Israel, Dark stars: the evolution of an idea, in 300 Years of Gravitation, edited by S.W. Hawking and W. Israel, Cambridge University Press, Cambridge, 1987, Chapter 7, pp. 199–276.Google Scholar
  10. [10]
    The discovery of binary pulsars is related in Hulse’s Nobel Lecture: R.A. Hulse, Reviews of Modern Physics 66 (1994), 699.CrossRefADSGoogle Scholar
  11. [11]
    For an introduction to the observational characteristics of pulsars, and their use in testing relativistic gravitation, see Taylor’s Nobel Lecture: J.H. Taylor, Reviews of Modern Physics 66 (1994), 711. See also Michael Kramer’s contribution to this Poincaré seminar.CrossRefADSGoogle Scholar
  12. [12]
    For an update on the observational characteristics of pulsars, and their use in testing general relativity, see the Living Review by I.H. Stairs, available at and the contribution by Michael Kramer to this Poincaré seminar.
  13. [13]
    For a recent update on tests of relativistic gravitation (and of tensor-scalar theories) obtained through the chronometry of binary pulsars, see G. Esposito-Farèse, grqc/0402007 (available on the general relativity and quantum cosmology archive at the address, and T. Damour and G. Eeposito-Farèse, in preparation. Figure 4 is adapted from these references.
  14. [14]
    For a review of the problem of the motion of two gravitationally condensed bodies in general relativity, up to the level where the effects connected to the finite speed by S.W. Hawking and W. Israel, Cambridge University Press, Cambridge, 1987, Chapter 6, pp. 128–198.Google Scholar
  15. [15]
    A. Einstein, Näherungsweise Integration der Feldgleichungen der Gravitation, Sitz. Preuss. Akad. Wiss. (1916), p. 688; ibidem, Über Gravitationswellen (1918), p. 154.Google Scholar
  16. [16]
    For a highly detailed introduction to these three problems, see K.S. Thorne Gravitational radiation, in 300 Years of Gravitation, edited by S.W. Hawking and W. Israel, Cambridge University Press, Cambridge, 1987, Chapter 9, pp. 330–458.Google Scholar
  17. [17]
  18. [18]
  19. [19]
  20. [20]
  21. [21]
    L. Blanchet et al., gr-qc/0406012; see also the Living Review by L. Blanchet, available at Scholar
  22. [22]
    Figure 5 is adapted from work by A. Buonanno and T. Damour, gr-qc/0001013.Google Scholar
  23. [23]
    F. Pretorius, Phys. Rev. Lett. 95 (2005), 121101, gr-qc/0507014; M. Campanelli et al., Phys. Rev. Lett. 96 (2006), 111101, gr-qc/0511048 J. Baker et al., Phys. Rev. D 73 (2006), 104002, gr-qc/0602026.CrossRefADSMathSciNetGoogle Scholar
  24. [24]
    For a particularly clear exposé of the development of the quantum theory of fields, see, for example, the first chapter ofS. Weinberg, The Quantum Theory of Fields, volume 1, Foundations, Cambridge University Press, Cambridge, 1995.Google Scholar
  25. [25]
    For an introduction to the theory of (super)strings see For a detailed (and technical) introduction to the theory see the books: K. Becker, M. Becker, and J.H. Schwarz, String Theory and M-theory: An Introduction, Cambridge University Press, Cambridge, 2006; B. Zwiebach, A First Course in String Theory, Cambridge University Press, Cambridge University Press, Cambridge, 1987; and J. Polchinski, String Theory, 2 high-energy physics) see also the site rs URL
  26. [26]
    For a detailed introduction to black hole physics see P.K. Townsend, gr-qc/9707012; for an entry into the vast literature on black hole entropy, see, for example, Bertrand Duplantier, and Vincent Rivasseau (Birkhäuser Verlag, Basel, 2004), pp. 227-264.Google Scholar
  27. [27]
  28. [28]
  29. [29]
    M. Born, Physics and Relativity, in Fünfzig Jahre Relativitätstheorie, Bern, 11–16 Juli 1955, Verhandlungen, edited by A. Mercier and M. Kervaire, Helvetica Physica Acta, Supplement 4 (1956), 244-260.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 2007

Authors and Affiliations

  • Thibault Damour
    • 1
  1. 1.Thibault DamourInstitut des Hautes Études ScientifiquesBures-sur-YvetteFrance

Personalised recommendations