f(R,Lm) gravity

By Tiberiu Harko, Francisco S. N. Lobo. Gravity, 2010

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We generalize the f(R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian Lm. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert–Einstein Lagrange density are also derived.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f9994b09058a6a4f3c63a49382d40903900feddf

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Citations in the corpus

Generalized Curvature-Matter Couplings in Modified Gravity (2014, methodology): “ity theory represent the maximal extension of the set of all gravitational theories constructed in a Riemann space and with the action depending on the Ricci scalar and the matter Lagrangian only. In [15], the gravitational ﬁeld equations of the f(R;L m) gravity theory in the metric formalism were o”