Scattering of Hawking photons as a barrier to particle absorption by black holes

Electromagnetic scattering interactions between photons emanating from a Schwarzschild black hole and an incident charged particle should generate a repulsive force between the particle and black hole. The net scattering cross-section is calculated here as a function of the mass M of the black hole and the mass m of the particle for scenarios in which the particle is point-like and initially stationary, with proper energy ε=m, at some location far from the black hole. It follows from comparing the repulsive scattering force to the corresponding gravitational force that, in order for the particle to be drawn to the black hole, ε/Tbh must be greater than a certain lower bound that is of the order 10−3 for spin-1/2 or spin-0 particles with unit-charge. Although the scattering restriction is weaker than the requirement ε/Tbh≫1 obtained independently from field-theoretic and thermodynamic treatments, the recurrence of a lower bound on the Boltzmann factor ε/Tbh in limitations on particle absorption suggests a physical unity whose nature is fundamentally thermodynamic.