Geodesically complete black holes in Lorentz-violating gravity

TL;DR

This paper systematically studies non-singular black hole spacetimes in Lorentz-violating gravity, introducing universal trapping horizons and classifying geodesically complete black holes with diverse scenarios like bouncing and evaporating black holes.

Contribution

It introduces the concept of universal trapping horizons for Lorentz-violating frameworks and classifies all possible geodesically complete black hole geometries in such theories.

Findings

Universal trapping horizons generalize trapping horizons in Lorentz-violating gravity.

Not all classes of black holes in Lorentz-invariant frameworks exist in Hořava-like frameworks.

Diverse geodesically complete black hole scenarios include bouncing, evaporating, and wormhole configurations.

Abstract

We present a systematic study of the geometric structure of non-singular spacetimes describing black holes in Lorentz-violating gravity. We start with a review of the definition of trapping horizons, and the associated notions of trapped and marginally trapped surfaces, and then study their significance in frameworks with modified dispersion relations. This leads us to introduce the notion of universally marginally trapped surfaces, as the direct generalization of marginally trapped surfaces for frameworks with infinite signal velocities (Ho\v{r}ava-like frameworks), which then allows us to define universal trapping horizons. We find that trapped surfaces cannot be generalized in the same way, and discuss in detail why this does not prevent using universal trapping horizons to define black holes in Ho\v{r}ava-like frameworks. We then explore the interplay between the kinematical part of Penrose's singularity theorem, which implies the existence of incomplete null geodesics in the presence of a focusing point, and the existence of multiple different metrics. This allows us to present a complete classification of all possible geometries that neither display incomplete physical trajectories nor curvature singularities. Our main result is that not all classes that exist in frameworks in which all signal velocities are realized in Ho\v{r}ava-like frameworks. However, the taxonomy of geodesically complete black holes in Ho\v rava-like frameworks includes diverse scenarios such as evaporating regular black holes, regular black holes bouncing into regular white holes, and hidden wormholes.