Non-thermal high-energy emissions from black holes by a relativistic capillary effect

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.