New regular 2+1 black hole solutions from bilocal gravity

We obtain new regular black hole solutions for an action in 2+1 dimensions with bilocal Ricci scalar and negative cosmological constant. Besides their connection to the cosmological constant, these solutions depend on a fundamental length due to their non-local nature. The effective profile densities that result from the non-local geometries have quasi-localized mass/energy since they are finite at the origin and their integration in all space is convergent. The black holes obtained are free of singularities and present one, two, or none horizons depending on the values of the involved parameters. The new solutions can have either an AdS, dS, or even a flat core. In the case of a de-Sitter core, it could represent a repulsive force coming from quantum effects. Although the resulting (effective) cosmological constant is positive near the origin, the classical (naked) counterpart is still negative thus precluding a cosmological horizon. We investigate the energy conditions of the effective source and determine the region where exotic energy should be found. Thermodynamic quantities are also computed. On the one hand, Gibbs's potential shows that both solutions are globally unstable, as in the BTZ case. On the other, we show that for small values of the horizon radius the Hawking temperature is negatively divergent but a finite size remnant can be defined where $T_H$ crosses zero. At this point, the heat capacity sign changes from negative to positive, indicating that the black holes are locally stable while irradiating. Thus, such a quantity, along with $T_H$, presents crucial differences with the BTZ black hole for small horizon radii where quantum effects become relevant. Finally, we analyze the bilocal black hole geodesics and find stable circular orbits for massless and massive particles, another feature absent in the BTZ case.