(Compactified) black branes in four dimensional f(R)-gravity

A new family of analytical solutions in a four dimensional static spacetime is presented for $f\left( R\right) $-gravity. In contrast to General Relativity, we find that a non trivial black string/ring solution is supported in vacuum power law $f\left( R\right) $-gravity for appropriate values of the parameters characterizing the model and when axisymmetry is introduced in the line element. For the aforementioned solution, we perform a brief investigation over its basic thermodynamic quantities.