Interpret the inner helicity-1-horizon singularity

Determine the physical meaning of the singular behavior that appears at an inner helicity-1 horizon for slowly moving Schwarzschild black holes in Einstein–aether theory at sufficiently large vector-mode speed.

Background

The paper studies dipolar aether perturbations describing a slowly moving Schwarzschild black hole in the decoupling limit of Einstein–aether theory. The perturbations are required to be regular at infinity and at the outer scalar and vector horizons, while additional inner vector horizons can occur for large vector-mode speed.

For sufficiently large vector-mode speed, the numerical solutions develop a singularity at an inner helicity-1 horizon located inside the universal horizon of the unperturbed black hole. Because this region is causally shielded from infinity, the singularity does not affect the sensitivity calculation, but its physical interpretation is left unresolved.

References

In particular, for large $s_V$, a singularity appears at the inner helicity-1 horizon $\xi_{V,\rm inner}>\xi_\star$ which does not allow one to extend the solution past this value. This singular behavior is visible in the red curves in Fig.~\ref{fig:B1}. Its physical meaning is unclear.

— Black hole sensitivity in Einstein--aether theory  (2610.00503 - Kidnew et al., 30 Sep 2026) in Section 3.2, immediately following Figures 1 and 2