Correct use of Platini's principle in gravitational theories

Details Correct use of Platini's principle in gravitational theories Correct use of Platini's principle in gravitational theories

Dec 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978mvsfa..19...57p&link_type=abstract

Moskovskii Universitet, Vestnik, Seriia III - Fizika, Astronomiia, vol. 19, Nov.-Dec. 1978, p. 57-59. In Russian.

Astronomy and Astrophysics

Astrophysics

Astrophysics, Cosmology, Gravitation Theory, Variational Principles, Canonical Forms, Einstein Equations, Functionals

Scientific paper

It is shown that the correct variational problem in metric theories of gravitation, based on independent variation over the coefficients of the affine connection and the metric coefficients, is the problem of finding the conditional extremum of a certain action integral. In the Einstein-Cartan theory, the field equations are derived on the basis of Palatini's variational principle, and the connectivity satisfies the condition of metricity, but this condition is not taken into account in the variational process. It is proposed instead that one take into account the condition of metricity from the very start in the Lagrangian in order to derive the field equations.

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