Global monopole in Palatini f (R ) gravity

We consider the space-time metric generated by a global monopole in an extension of general relativity (GR) of the form f (R )=R -λ R². The theory is formulated in the metric-affine (or Palatini) formalism, and exact analytical solutions are obtained. For λ <0 , one finds that the solution has the same characteristics as the Schwarzschild black hole with a monopole charge in Einstein's GR. For λ >0 , instead, the metric is more closely related to the Reissner-Nordström metric with a monopole charge and, in addition, it possesses a wormhole-like structure that allows for the geodesic completeness of the space-time. Our solution recovers the expected limits when λ =0 and also at the asymptotic far limit. The angular deflection of light in this space-time in the weak field regime is also calculated.