We provide an algorithm that shows how to decouple gravitational sources in pure Lovelock gravity. This method allows to obtain several new and known analytic solutions of physical interest in scenarios with extra dimensions and with presence of higher curvature terms. Furthermore, using our method, it is shown that applying the minimal geometric deformation to the Anti de Sitter space time it is possible to obtain regular black hole solutions.

In this work two new families of non-singular or regular black hole solutions are displayed. These black holes behave as de Sitter space near its center and have a well defined AdS asymptotic region...

In this work it is shown that the thermodynamics of regular black holes with a cosmological horizon, which are solutions of Lovelock gravity, determines that they must evolve either into a state where the black hole and cosmological horizons have reached thermal equilibrium or into an extreme black hole geometry where the black hole and cosmological horizons have merged. This differs from the behavior of Schwarzschild de Sitter geometry which evolves into a de Sitter space, the ground state of the space of solutions. This occurs due to a phase transition of the heat capacity of the black hole horizon. To perform that analysis it is shown that at each horizon a local first law of thermodynamics can be obtained from the gravitational equations.

We provide a new regular black hole solution in 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 the usual first law is recovered. The effectiveness of the formalism used to compute the mass of our regular black holes in dimensions suggests the potential applicability of this method to calculate the mass of other models of regular black holes in dimensions.