Exploring Cosmic Rays from Gravity-Limited Acceleration at Supermassive Black Holes

We show that horizon-scale magnetic fields around supermassive black holes (SMBHs), only limited by gravity, yield a universal, model-independent ceiling on electromagnetic energy density. For rotating SMBHs, this field enables particle acceleration up to $\sim \text{\hspace{0.17em}⁣}{10}^{27}$,eV set solely by fundamental constants. We identify a parameter space in accretion rate and magnetic field strength in which quiescent nuclei simultaneously satisfy the transparency conditions for Ultra-High-Energy Cosmic Rays (UHECR) escape and the field requirements for reaching Ultra-High Energies (UHE), naturally complementing photon-rich Active Galactic Nuclei (AGN), which favor neutrino production but suppress UHECR escape. We observe that, when including curvature energy losses, the energy of the primaries scales weakly as $E_{\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{v}}\text{\hspace{0.17em}⁣}\propto \text{\hspace{0.17em}⁣}{M}^{1\mathrm{/}4}$ and allows to achieve UHE across different compositions and SMBHs masses (${10}^6$–${10}^{10}{M}_{\odot }$), without requiring extreme spins or super-Eddington accretion. A cross-correlation of the Pierre Auger Observatory (PAO) public data with galaxies hosting reliably measured SMBH masses, separating AGN from quiescent hosts, reveals marginal local excesses ($\lesssim \text{\hspace{0.17em}⁣}2.8\sigma$) consistent with isotropy after correcting for the look-elsewhere effect. The framework provides a direct link between black-hole physics and the maximum energies of cosmic particles, and defines concrete observational tests for next-generation UHECR datasets.