Abstract
The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed.
Similar content being viewed by others
References
C. N. Yang and R. L. Mills,Phys. Rev. 96, 191 (1954).
R. Utiyama,Phys. Rev. 101, 1597 (1956).
T. W. B. Kibble,J. Math. Phys. 2, 212 (1961).
D. W. Sciama, inRecent Developments in General Relativity (Pergamon, New York, and PWN-Polish Scientific, Warsaw, 1962).
Y. M. Cho,Phys. Rev. D,14, 2521, 3335, and 3341 (1976).
F. Mansouri and L. N. Chang,Phys. Rev. D,13, 3192 (1976).
K. Hayashi and T. Nakano,Progr. Theor. Phys. 38, 491 (1967).
C. N. Yang,Phys. Rev. Lett. 33, 445 (1974).
R. Burghardt,Acta. Phys. Austr. 38, 327 (1973); andActa. Phys. Austr. 39, 31 and 127 (1974).
M. Camezind,J. Math. Phys. 16, 1023 (1975); andGen. Rel. Grav. 8, 103 (1977).
E. A. Lord,Phys. Lett. 65A, 1 (1978).
J. P. Harnad and R. B. Pettitt,J. Math. Phys. 17, 1827 (1976).
P. von der Hyde,Phys. Lett. 58A, 141 (1976).
M. Carmeli and S. Malin,Ann. of Phys. 103, 208 (1977).
Y. M. Cho and P. S. Yang,Phys. Rev. D,12, 3789 (1975).
A. G. Agnese and P. Calvini,Phys. Rev. D,12, 3800 and 3804 (1975).
F. W. Hehl, P. von der Hyde, G. D. Kerlick, and J. M. Nester,Rev. of Mod. Phys. 48, 393 (1976).
D. Derbes,Il Nuovo Cimento 45B, 31 (1978).
A. Trautman,Rep. Math. Phys. 1, 29 (1979);Rep. Math. Phys. 10, 297 (1976).
A. Lichnerowicz,Gen. Rel. Grav. 1, 235 (1971).
W. Drechsler and M. E. Mayer,Fiber Bundle Techniques in Gauge Theory (Lecture Notes in Physics) (Springer-Verlag, Berlin, 1977).
E. Lubkin,Ann. of Phys. 23, 233 (1963).
C. Lanczos,Rev. Mod. Phys. 34, 379 (1962).
W. K. Atkins, Ph.D. Dissertation, unpublished.
W. K. Atkins and W. R. Davis,Il Nuovo Cimento,59B, 116 (1980).
J. A. Schouten,Ricci Calculus (Springer-Verlag, Berlin, 1954).
N. Rosen,Found. Phys. 10, 673 (1980).
J. Schwinger,Particles, Sources, and Fields, Vol. I (Addison-Wesley, Reading, Mass., 1970), pp. 189–190.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Atkins, W.K. A fundamental quadratic variational principle underlying general relativity. Found Phys 13, 545–552 (1983). https://doi.org/10.1007/BF00729515
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00729515