Capture of particles from plunge orbits by a black hole

Photon and "parabolic" particle orbits around a Kerr-Newman black hole are considered, both for uncharged particles moving along geodesics and for charged particles under the influence of the Lorentz force (neglecting radiative processes). Investigation of the radial equation of motion gives conditions under which a photon or particle is captured from a "plunge" orbit when incident from a large distance; the cross sections and accreted angular momenta are calculated for various fluxes of particles incident on the black hole. For example, the cross section of an extreme Kerr ($a=1\mathrm{}$) black hole to an isotropic flux of particles is 0.90 of that for a Schwarzschild hole, and the accreted angular momentum per unit mass of swallowed flux is -0.828 leading to rapid spin-down of the hole. The periastra of "escape" orbits are considered, and also the minimum periastron corresponding to the unstable spherical orbit that divides plunge and escape orbits. The evolution of the spin and charge of a black hole accreting particles and photons is discussed, including that of primordial black holes. It is shown that such black holes may be of the Schwarzschild type having spun-down due to consumption of radiation and particles at early times and subsequent neutralization in an ionized intergalactic medium. The statistics of proton and electron capture by the smallest surviving primordial black holes, $M={10}^{15}$ g, suggests that they are most likely to be found possessing a single quantum of positive charge.