Lorentz-Violating (Regular) Black Holes in Einstein Gravity

We introduce a minimally coupled dark sector based on a nonlinear electrodynamics to generate regular spacetime textures that interpolate from a regular core to an asymptotic Lorentz-violating conical geometry. This construction provides a simple mechanism, in Einstein gravity with minimally coupled matter, for obtaining Lorentz-violating Schwarzschild and Reissner-Nordstr\"om black holes. The framework further allows us to construct Lorentz-violating regular black holes, including the Bardeen and Hayward black holes, as well as a class of electrically-charged regular black holes.