Regular Black Holes and Horizonless Ultra-Compact Objects in Lorentz-Violating Gravity

Abstract: There is growing evidence that Ho\v{r}ava gravity may be a viable quantum theory of gravity. It is thus legitimate to expect that gravitational collapse in the full, non-projectable version of the theory should result in geometries that are free of spacetime singularities. Previous analyses have shown that such geometries must belong to one of the following classes: simply connected regular black holes with inner horizons; non-connected black holes "hiding" a wormhole mouth (black bounces); simply connected or non-connected horizonless compact objects. Here, we consider a singular black hole in the low-energy limit of non-projectable Ho\v{r}ava gravity, i.e. khronometric theory, and describe examples of its possible "regularisations", covering all of the viable classes. To our knowledge, these examples constitute the first instances of black holes with inner universal horizons, of black bounces and of stars with a de Sitter core in the context of Lorentz-violating theories of gravity.