Abstract
We consider the domain of applicability of general relativity (GR), as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations. We argue that, as it stands, GR is deficient whether it is treated as a microscopic or a macroscopic theory of gravity. We briefly discuss some recent attempts at removing this shortcoming through the construction of a macroscopic theory of gravity. We point out that such macroscopic extensions of GR are likely to be nonunique and involve non-Riemannian geometrical frameworks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
G. F. R. Ellis, in General Relativity and Gravitation, B. Bertotti, F. de Felici, and A. Pascolini, eds. (Reidel, Dordrecht, 1981), p. 215.
D. W. Sciama, Modern Cosmology (Cambridge University Press, Cambridge, 1971), Chap. 8.
J. Ehlers, in Relativity, Astrophysics and Cosmology, W. Israel, ed. (Reidel, Dordrecht, 1973).
J. Ehlers, F. A. E. Pirani, and A. Schild, in General Relativity. Papers in Honour of J. L. Synge, L. O'Raifeartaigh, ed. (Clarendon, Oxford, 1972), p. 63.
R. K. Tavakol and G. F. R. Ellis, Phys. Lett. A 130, 217 (1988).
A. Coley and R. K. Tavakol, Gen. Relat. Gravit. 24, 835 (1992).
G. F. R. Ellis, “Observations and cosmological models,” Preprint 1995/1, University of Cape Town, 1995.
C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 1993).
M. F. Shirokov and I. Z. Fisher, Astron. Zh. 39, 899 (1962) ( in Russian) [English translation: Sov. Astron. A.J. 6, 699 (1963) ].
A. Hemmerich, Astron. Astrophys. 185, 1 (1987).
R. M. Zalaletdinov, Gen. Relat. Gravit. 24, 1015 (1993).
A. Krasiński, Inhomogeneous Cosmological Models (Cambridge University Press, Cambridge, 1997).
J. Ehlers, in Ninth Texas Symposium on Relativistic Astrophysics, J. Ehlers, J. J. Perry, and M. Walker, eds. (New York Academy of Sciences, New York, 1980), p. 279.
P. Havas, in Isolated Gravitating Systems in General Relativity, J. Ehlers, ed. (North–Holland, Amsterdam, 1979), p. 74.
P. Havas and J. N. Goldberg, Phys. Rev. 128, 398 (1962).
J. Ehlers, in General Relativity and Gravitation, M. A. H. MacCallum, ed. (Cambridge University Press, Cambridge, 1987), p. 61.
R. H. Schattner, “The structure of extended bodies in general relativity,” Ph.D. Thesis, University of Mü nich, unpublished.
L. Infeld and A. Schild, Rev. Mod. Phys. 21, 408 (1949).
J. M. Nevin, Gen. Relat. Gravit. 27, 397 (1995).
A. Papapetrou, Lectures on General Relativity (Reidel, Dordrecht, 1974).
W. G. Dixon, in Isolated Gravitating Systems in General Relativity, J. Ehlers, ed. (North–Holland, Amsterdam, 1979), p. 156.
V. Fock, The Theory of Space Time and Gravitation (Pergamon, London, 1959).
T. Damour, in Gravitational Radiation, N. Deruelle et al., eds. (North–Holland, Amsterdam, 1983), p. 59.
J. Ehlers, Akad. Wiss. Lit. (Mainz) Abhandl. Math.–Nat. Kl. 11, 792 (1961) [English translation: Preprint, 1993/8, University of Cape Town, 1993].
H. A. Lorentz, The Theory of Electrons (Teubner, Leipzig, 1916).
S. T. deGroot and L. G. Suttorp, Foundations of Electrodynamics (North–Holland, Amsterdam, 1972).
L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Pergamon Press, New York, 1975).
B. Mashhoon, Phys. Lett. A 143, 176 (1990).
S. Ikeda, Found. Phys. 13, 629 (1983).
M. N. Mahanta, Int. J. Theor. Phys. 23, 569 (1984).
F. W. Hehl, Found. Phys. 15, 451 (1985).
N. Bohr and L. Rosenfeld, Mat.–Fys. Medd. Dan. Vid. Selsk. 12, 8 (1933).
B. S. DeWitt, in General Relativity, An Einstein Centenary Survey, S. W. Hawking and W. Israel, eds. (Cambridge University Press, Cambridge, 1979), p. 680.
B. Mashhoon, Phys. Lett. A 145, 147 (1990).
R. K. Tavakol and N. Van den Bergh, Gen. Relat. Gravit. 18, 849 (1986).
I. W. Roxburgh, Gen. Relat. Gravit. 23, 1071 (1991).
J. Ehlers, in Isolated Gravitating Systems in General Relativity, J. Ehlers, ed. (North–Holland, Amsterdam, 1979), p. 1.
W. Israel, in General Relativity. Papers in Honour of J.L. Synge, L. O'Raifeartaigh, ed. (Clarendon, Oxford, 1972), p. 201.
D. Kramer, H. Stephani, M. MacCallum, and E. Herlt, Exact Solutions of Einstein's Field Equations (Deutscher Verlag der Wissenschaften and Cambridge University Press, Berlin and Cambridge, 1980).
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
R. M. Zalaletdinov and R. K. Tavakol, in progress.
B. Carter, in General Relativity, An Einstein Centenary Survey, S. W. Hawking and W. Israel, eds. (Cambridge University Press, Cambridge, 1979), p. 294.
J. Ehlers, “The Newtonian limit of general relativity,” Preprint 1989/1, University of Cape Town, 1989.
W. K. H. Panowsky and M. Phillips, Classical Electricity and Magnetism (Addison–Wesley, Reading, Massachusetts, 1962).
S. W. Hawking and G. F. R. Ellis, The Large–Scale Structure of Spacetime (Cambridge University Press, Cambridge, 1973).
A. Lichnerowicz, Relativistic Hydrodynamics and Magnetodynamics (Benjamin, New York, 1967).
L. Rosenfeld, Theory of Electrons (Dover, New York, 1965).
R. M. Zalaletdinov, Gen. Relat. Gravit. 25, 673 (1993)
R. M. Zalaletdinov, Bull. Astron. Soc. India 25, 401 (1997).
D. C. Leslie, Developments in the Theory of Turbulence (Clarendon, Oxford, 1973).
R. M. Zalaletdinov, in Proceedings, International Symposium on Experimental Gravitation, M. Karim and A. Qadir, eds. (Institute of Physics, Bristol, 1994), p. A363.
R. M. Zalaletdinov, in Inhomogeneous Cosmological Models, A. Molina and J. M. M. Senovilla, eds. (World Scientific, Singapore, 1995), p. 91.
R. A. Isaacson, Phys. Rev. 166, 1272 (1968).
P. Szekeres, Ann. Phys. (N.Y.) 64, 599 (1971).
S. Bildhauer and T. Futamase, Gen. Relat. Gravit. 23, 1251 (1991).
Rights and permissions
About this article
Cite this article
Tavakol, R., Zalaletdinov, R. On the Domain of Applicability of General Relativity. Foundations of Physics 28, 307–331 (1998). https://doi.org/10.1023/A:1018761005186
Issue Date:
DOI: https://doi.org/10.1023/A:1018761005186