Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-07-26
Mod.Phys.Lett.A26:1467-1480,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, no figures; v2, revised and corrected version; new Section added
Scientific paper
10.1142/S0217732311035869
We derive the field equations and the equations of motion for massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We derive the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra-force is obtained in terms of the matter-geometry coupling functions and of their derivatives. Generally, the motion is non-geodesic, and the extra force is orthogonal to the four-velocity.
Harko Tiberiu
Koivisto Tomi S.
Lobo Francisco S. N.
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