# Spherically symmetric spacetimes in fR gravity theories - General Relativity and Quantum Cosmology

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Abstract: We study both analytically and numerically the gravitational fields of starsin fR gravity theories. We derive the generalized Tolman-Oppenheimer-Volkovequations for these theories and show that in metric fR models theParameterized Post-Newtonian parameter $\gamma { m PPN} = 1-2$ is a robustoutcome for a large class of boundary conditions set at the center of the star.This result is also unchanged by introduction of dark matter in the SolarSystem. We find also a class of solutions with $\gamma { m PPN} \approx 1$ inthe metric $fR=R-\mu^4-R$ model, but these solutions turn out to be unstableand decay in time. On the other hand, the Palatini version of the theory isfound to satisfy the Solar System constraints. We also consider compact starsin the Palatini formalism, and show that these models are not inconsistent withpolytropic equations of state. Finally, we comment on the equivalence betweenfR gravity and scalar-tensor theories and show that many interesting PalatinifR gravity models can not be understood as a limiting case of aJordan-Brans-Dicke theory with $\omega \to -3-2$.

Autor: Kimmo Kainulainen, Johanna Piilonen, Vappu Reijonen, Daniel Sunhede

Fuente: https://arxiv.org/

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