A new model of regular black hole in (2 + 1) dimensions

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We provide a new regular black hole solution in (2 + 1) dimensions with the presence of matter fields in the energy momentum tensor. The inclusion of our proposed energy density plus a negative cosmological constant allows that the solution can have both flat as de Sitter or Anti-de Sitter core. This latter is a proper characteristic of our solution, because other models of regular black holes have only a single type of core. Since the first law of thermodynamics for regular black holes is modified by the presence of the matter fields, we provide a new version of the first law, where a local definition of the variation of energy is defined, and where the entropy and temperature are consistent with the ones previously known in the literature. At the hypothetical limit when the horizon radius r+ → ∞ the usual first law dM = TdS is recovered. The effectiveness of the formalism used to compute the mass of our regular black holes in (2 + 1) dimensions suggests the potential applicability of this method to calculate the mass of other models of regular black holes in d ≥ 4 dimensions.