Black hole horizons at the extremal limit in Lorentz-violating gravity

TL;DR

This paper investigates the nature of universal horizons in Lorentz-violating gravity theories as they approach the extremal limit, revealing that extremal Killing horizons act as degenerate universal horizons.

Contribution

It introduces a decoupling limit approach to analyze the behavior of universal horizons at the extremal limit in Lorentz-violating gravity theories.

Findings

Extremal Killing horizons serve as degenerate universal horizons at the extremal limit.

Universal horizons can exist even when the Killing vector is null, not spacelike.

The study clarifies the nature of horizons in Lorentz-violating gravity near extremality.

Abstract

Lorentz-violating gravity theories with a preferred foliation can have instantaneous propagation. Nonetheless, it has been shown that black holes can still exist in such theories and the relevant notion of an event horizon has been dubbed `universal horizon'. In stationary spacetimes the universal horizon has to reside in a region of spacetime where the Killing vector associated with stationarity is spacelike. This raises the question of what happens to the universal horizon in the extremal limit, where no such region exists anymore. We use a decoupling limit approximation to study this problem. Our results suggest that at the extremal limit, the extremal Killing horizon appears to play the role of a degenerate universal horizon, despite being a null and not a spacelike surface, and hence not a leaf of the preferred foliation.