We consider the space-time metric generated by a global monopole in an extension of General Relativity (GR) of the form f (R) = R − λR 2 . 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 spacetime in the weak field regime is also calculated. *

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We have analyzed the effects of a simple wormhole, known as the Ellis–Bronnikov-type wormhole, on a scalar field, where, analytically, we determine solutions of bound states and show that the relativistic energy profile of this scalar field is drastically influenced by the topology of space-time characterized by the presence of a global monopole. Before this analysis, we investigated the effects of this background on the deflection of light, which is influenced by the parameters associated with the wormhole throat and the topological defect.

In this paper we consider two different nonlinear σ-models minimally coupled to Eddington-inspired Born-Infeld gravity. We show that the resultant geometries represent minimal modifications with respect to those found in GR, though with important physical consequences. In particular, wormhole structures always arise, though this does not guarantee by itself the geodesic completeness of those space-times. In one of the models, quadratic in the canonical kinetic term, we identify a subset of solutions which are regular everywhere and are geodesically complete. We discuss characteristic features of these solutions and their dependence on the relationship between mass and global charge.