f(R, T) Gravity

By Tiberiu Harko, Francisco S. N. Lobo, Shin’ichi Nojiri, S. D. Odintsov. Gravity, 2011

1,422 citations recorded by the source corpus.

We consider $f(R,T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the trace of the stress-energy tensor $T$. 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 stress-energy tensor. Generally, the gravitational field equations depend on the nature of the matter source. The field equations of several particular models, corresponding to some explicit forms of the function $f(R,T)$, are also presented. An important case, which is analyzed in detail, is represented by scalar field models. We write down the action and briefly consider the cosmological implications of the $f(R,{T}^{\ensuremath{\phi}})$ models, where ${T}^{\ensuremath{\phi}}$ is the trace of the stress-energy tensor of a self-interacting scalar field. The equations of motion of the test particles are also obtained from a variational principle. The motion of massive test particles is nongeodesic, and takes place in the presence of an extra-force orthogonal to the four velocity. The Newtonian limit of the equation of motion is further analyzed. Finally, we provide a constraint on the magnitude of the extra acceleration by analyzing the perihelion precession of the planet Mercury in the framework of the present model.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/da79a5e162a0e9526228fd132ce2575a5cf17741

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Citations in the corpus

Generalized Curvature-Matter Couplings in Modified Gravity (2014, methodology): “For the specific case of a traceless energy-momentum tensor, T = 0, for instance, when the electromagnetic field is involved, the gravitational field equations for the f(R, T ) theory [14] reduce to that of the field equations for f(R) gravity and all non-minimal couplings of gravity to the matter f”
Hybrid Metric-Palatini Gravity (2015, background): “Other extensions of the f(R) framework modify the coupling of matter to gravity by defining an action which depends linearly [39] or nonlinearly upon the matter Lagrangian [40–47], or its trace [48–50].”