  Gravitational spin-orbit interactions induce a relativistic capillary effect
along open magnetic flux-tubes, that join the event horizon of a spinning black
hole to infinity. It launches a leptonic outflow from electron-positron pairs
created near the black hole, which terminates in an ultra-relativistic Alfv\'en
wave. Upstream to infinity, it maintains a clean linear accelerator for baryons
picked-up from an ionized ambient environment. We apply it to the origin of
UHECRs and to spectral energy correlations in cosmological gamma-ray bursts.
The former is identified with the Fermi-level of the black hole event horizon,
the latter with a correlation $E_pT_{90}^{1/2}\simeq E_\gamma$ in HETE-II and
Swift data.
