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We study Born-Infeld gravity coupled to an anisotropic fluid in a static,spherically symmetric background. The free function characterizing the fluid isselected on the following grounds: i) recovery of the Reissner-Nordstr\"omsolution of GR at large distances, ii) fulfillment of classical energyconditions and iii) inclusion of models of nonlinear electrodynamics asparticular examples. Four branches of solutions are obtained, depending on thesigns of two parameters on the gravity and matter sectors. On each branch, wediscuss in detail the modifications on the innermost region of thecorresponding solutions, which provides a plethora of configurations, includingnonsingular black holes and naked objects, wormholes and de Sitter cores. Theregular character of these configurations is discussed according to thecompleteness of geodesics and the behaviour of curvature scalars.

Nonsingular black holes, wormholes, and de Sitter cores from anisotropic fluids