BTZ black holes with higher curvature corrections in the 3D Einstein-Lovelock theory

The regularization procedure for getting the four-dimensional nontrivial Einstein-Gauss-Bonnet effective description of gravity and its Lovelock generalization has been recently developed. Here we propose the regularization for the three-dimensional gravity, which is based on the rescaling of the coupling constants and, afterward, taking the limit $D \to 3$. We obtain the generalization of the Ba\~nados-Teitelboim-Zanelli solution in the presence of the higher curvature (Gauss-Bonnet and Lovelock) corrections of any order. The obtained general solution shows a peculiar behavior: The event horizon is allowed not only for asymptotically anti-de Sitter spacetimes, but also for the de-Sitter and flat cases, when the Gauss-Bonnet coupling constant is negative. The factor of the electric charge is analyzed as well for various branches of the solution and the Hawking temperature is obtained.