Regular reduction of relativistic theories of gravitation with a quadratic Lagrangian

Details Regular reduction of relativistic theories of gravitation with a quadratic Lagrangian Regular reduction of relativistic theories of gravitation with a quadratic Lagrangian

Dec 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvd..32.3128b&link_type=abstract

Physical Review D (Particles and Fields), Volume 32, Issue 12, 15 December 1985, pp.3128-3135

Mathematics

Dynamical Systems

30

Gravity In More Than Four Dimensions, Kaluza-Klein Theory, Unified Field Theories, Alternative Theories Of Gravity

Scientific paper

We consider those relativistic theories of gravitation which generalize Einstein's theory in the sense that their field equations derive from a scalar Lagrangian which, besides the matter term, contains a linear combination of the Ricci scalar, its square, and the square of the Ricci tensor. Using a generalization of a technique which has been used to deal with some dynamical systems, we regularly and covariantly reduce the corresponding fourth-order differential equations to second-order ones. We examine, in particular, at a low order of approximation, these reduced equations in cosmology, and for static and spherically symmetric interior solutions with constant density.

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