Abstract
“Alternative gravitational theories” based on Lagrangian densities that depend in a nonlinear way on the Ricci tensor of a metric are considered. It is shown that, provided certain weak regularity conditions are met, any such theory is equivalent, from the Hamiltonian point of view, to the standard Einstein theory for a new metric (which, roughly speaking, coincides with the momentum canonically conjugated to the original metric), interacting with external matterfields whose nature depends on the original Lagrangian density.
Similar content being viewed by others
References
Kerner, R. (1982).Gen. Rel. Grav.,14(5), 453–469.
Hehl, F. W., Nitsch, J., and Von Der Heyde, P. (1980). InGeneral Relativity and Gravitation. One Hundred Years after the Birth of Albert Einstein, vol. 1, A. Held, (Plenum Press, New York), pp. 329–355.
Weyl, H. (1918).Raum-Zeit-Materie, 1st–3rd ed. (Springer, Berlin); (1950). 4th ed. (Dover, New York).
Ferraris, M., Francaviglia, M., and Reina, C. (1984). InActas de los Encuentros Relativistas Españoles 1983 (Servei de Publicacions, Palma de Mallorca), p. 153–184.
Ferraris, M., Francaviglia, M., and Reina, C. (1984). InAtti del V° Convegno Nazionale di Relatività Generale e Fisica della Gravitazione, M. Anile, S. Motta, S. Pluchino, eds. (Tipografia Universitaria, Catania).
Ferraris, M. (1984). InProceedings of the Journées Relativistes 1983, S. Benenti, M. Ferraris, M. Francaviglia, eds. (Tecnoprint, Bologna) p. 125–153.
Ferraris, M. and Kijowski, J. (1983).Rend. Sem. Mat. Univ. Politec. Torino,43, 169–201; (1982).Gen. Rel. Grav.,14, 2, 165–180; (1981).Lett. Math. Phys.,5, 2, 127–135; (1982).Gen. Rel. Grav.,14, 1, 37–47.
Martellini, M. (1983).Phys. Rev. Lett.,51, 3, 152–155; (1984).Phys. Rev.,D29, 12, 2746–2755.
Eddington, A. S. (1924).The Mathematical Theory of Relativity, 2nd ed. (Cambridge University Press, Cambridge).
Einstein, A. (1923).Sitzungsber. Preuss. Akad. Wiss. (Berlin), 137–140.
Ferraris, M. (1986). InAtti del 6° Convegno Nazionale di Relatività Generale e Fisica della Gravitazione, M. Modugno, ed. (Tecnoprint, Bologna).
Higgs, P. W. (1959).Nuovo Cim.,11, 6, 816–820.
Kijowski, J. (1978).Gen. Rel. Grav.,9, 10, 857–877; (1979).A Symplectic Framework for Field Theories, Lecture Notes in Physics 107 (Springer-Verlag, Berlin).
Magnano, G., Ferraris, M., and Francaviglia, M., (1987). (preprint).
Weinberg, S. (1972).Gravitation and Cosmology (John Wiley & Sons Inc., New York).
Teyssandier, P., and Tourrenc, Ph. (1983).J. Math. Phys.,24, 12, 2793–2799.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Magnano, G., Ferraris, M. & Francaviglia, M. Nonlinear gravitational Lagrangians. Gen Relat Gravit 19, 465–479 (1987). https://doi.org/10.1007/BF00760651
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00760651