Summary
A new theory of gravitation is presented in which the righ-hand side of the field equations contains the gravitational-field stress-energy tensort νμ . The crucial new information leading to this construction is the demonstration that the two basic differential identities of space-time geometry (that of Bianchi and that of Freud) require atrue gravitational field stress-energy tensort νμ which must be added to the matter tensor τ νμ . Otherwise, the two identities clash and lead to a mathematical overdetermination which creates insurmountable internal difficulties for the curved-space-time theory of gravitation as a whole.
Similar content being viewed by others
References
E. Schrödinger:Phys. Z.,19, 4 (1918).
H. Bauer:Phys. Z.,19, 163 (1918).
H. Yilmaz:Proceedings of the International Symposium on Spacetime Symmetries (Wigner Symposium), edited byY. S. Kim andW. W. Zachary (North-Holland, Amsterdam, 1989).
A. Einstein:Ann. Phys. (Leipzig),49, (1916). See eqs. (56) and (57).
A. Einstein:Phys. Z,19, 115 (1918).
H. Yilmaz:Ann. Phys. N.Y. Acad. Sci.,480, 625 (1986);Int. J. Theor. Phys.,21, 871 (1982);Phys. Lett. A,92, 377 (1982).
H. Yilmaz:Phys. Rev.,111, 1417 (1958);Ann. Phys. (N.Y.),104, 414 (1976).
D. Hilbert:Gött. Nachr.,3, 394 (1915);P. A. M. Dirac.:General Theory of Relativity (J. Wiley, New York, N.Y., 1975).
P. Freud:Ann. Math.,40, 417 (1939).
W. Pauli:Theory of Relativity (Dover Publications Co., New York, N.Y., 1958), p. 70, 216.
M. Carmeli, E. Leibowitz andN. Nissani:Gravitation (World Scientific, Singapore, 1990), p. 49–62.
L. D. Landau andE. M. Lifshitz:Classical Theory of Fields (Pergamon Press, London, 1975), 4 ed., pp. 280.
H. Yilmaz:Nuovo Cimento Lett.,7 337 (1973); see also ref. [6] above.
B. O. J. Tupper:Nuovo Cimento B,19, 135 (1974);Nuovo Cimento Lett.,14, 627 (1974).
H. P. Robertson andT. W. Noonan:Relativity and Cosmology (W. B. Saunders, Philadelphia, Penn., 1968), p. 239.
B. De Wit andJ. Smith:Field Theory in Particle Physics, Vol. 1 (North-Holland, 1986), p. 295.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yilmaz, H. Toward a field theory of gravitation. Nuov Cim B 107, 941–960 (1992). https://doi.org/10.1007/BF02899296
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02899296