Clarify the physical implications of the fine-tuned universal-horizon condition

Determine whether the numerical relation between the scalar-mode speed and vector-mode speed that preserves a universal horizon for a slowly moving Schwarzschild black hole in Einstein–aether theory has additional physical implications.

Background

The paper finds that motion generally destroys the universal horizon present in a static Schwarzschild black hole. It identifies two exceptions: the hypersurface-orthogonal khrono-metric limit with infinite vector-mode speed, and a special numerical relation between the scalar- and vector-mode speeds.

The authors do not derive or characterize any broader significance of the second, fine-tuned relation. They explicitly leave unresolved whether it is associated with other physical consequences in Einstein–aether theory.

References

The first choice is the limit of infinite vector \ae ther waves speed $s_V$, in which case the \AE-theory reduces to the khrono-metric model with hypersurface-orthogonal \ae ther. The second choice corresponds to a special numerical relation between $s_V$ and the speed of scalar \ae ther waves $s_S$. It would be interesting to understand if this latter relation has any other physical implications. We leave this question for future studies.

— Black hole sensitivity in Einstein--aether theory  (2610.00503 - Kidnew et al., 30 Sep 2026) in Section 6, Conclusions