Universal Horizons without Hypersurface Orthogonality

Abstract

A key consequence of Lorentz-violating gravity is the emergence of modified dispersion relations implying the absence of a universal maximum propagation speed. This challenges the conventional notion of the event horizon as a causal boundary common to all degrees of freedom. However, certain solutions in these theories exhibit \emph{universal horizons} -- surfaces capable of trapping signals of arbitrarily high speed, thereby restoring the notion of black hole. Previous studies have extensively characterised universal horizons in settings where Lorentz violation is encoded via a hypersurface-orthogonal \ae{}ther. In this work, we explore the possibility of extending this concept to more general cases where hypersurface orthogonality is relaxed. To do so, we construct a candidate trapping surface and analyse its causal properties using a general model for Lorentz-violating matter. We find that, in addition to the standard conditions associated to universal horizons, a local vanishing of the \ae{}ther's twist is also necessary. We then provide an explicit example of such a universal horizon by suitably deforming the \ae{}ther flow in a stealth Kerr solution recently found in Einstein--\ae{}ther theory. Moreover, we analyse the behaviour of trajectories which are not analytical at the universal horizon and discuss the implications of our findings for Hawking radiation. While our analysis is motivated by Einstein-\ae{t}her gravity, our results apply to broader classes of Lorentz-violating theories, further supporting the relevance of black hole phenomenology in these frameworks.