Gravity limits the kinetic energy of a massive elementary particle

Abstract

In this note, I argue that tidal effects generically limit the kinetic energy of a single massive elementary particle in the vicinity of a compact object. As the kinetic energy is increased, the differences in the tidal potential over a Compton wavelength will at some point exceed the rest mass of the particle. Above the threshold, one expects tidal effects to disrupt single-particle states, and in turn, one might expect an incident particle scattering off a compact object with an energy significantly exceeding the threshold to result in a shower of lower energy particles. A calculation reveals that the threshold for neutrinos scattering off a $10M_{\odot }$ black hole within three Schwarzschild radii is roughly $1\text{GeV}$.

Comments: 2 pages. v2: Major changes. Calculations unchanged, major improvements to discussion regarding interpretation, and a strong assumption was relaxed. Conclusions changed accordingly