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In this paper we investigate spherically symmetric vacuum solutions of $f(R)$gravity in a higher dimensional spacetime. With this objective we construct asystem of non-linear differential equations, whose solutions depend on theexplicit form assumed for the function $F(R)=\frac{df(R)}{dR}$. We explicitshow that for specific classes of this function exact solutions from the fieldequations are obtained; also we find approximated results for the metric tensorfor more general cases admitting $F(R)$ close to the unity.

Spherically symmetric vacuum solutions of modified gravity theory in higher dimensions