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This paper investigates a new class of regular black hole solutions in (2 +1)-dimensions by introducing a generalization of the quasi-localized mattermodel proposed by Estrada and Tello-Ortiz. Initially, we try to physicallyinterpret the matter source encoded in the energy-momentum tensor asoriginating from nonlinear electrodynamics. We show, however, that the requiredconditions for the quasi-locality of the energy density are incompatible withthe expected behavior of nonlinear electrodynamics, which must tend toMaxwell's theory on the asymptotic limit. Despite this, we propose ageneralization for the quasi-localized energy density that encompasses theexisting models in the literature and allows us to obtain a class of regularblack hole solutions exhibiting remarkable features on the event horizons andtheir thermodynamic properties. Furthermore, since the usual version of thefirst law of thermodynamics, due to the presence of the matter fields, leads toincorrect values of entropy and thermodynamics volume for regular black holes,we propose a new version of the first law for regular black holes.

A new class of regular black hole solutions with quasi-localized sources of matter in $(2 + 1)$ dimensions