  A novel generalization of photon surfaces to the case of massive charged
particles is given for spacetimes with at least one isometry, including
stationary ones. A related notion of glued massive particle surfaces is also
defined. These surfaces join worldlines parametrized by a family of independent
conserved quantities and naturally arise in integrable spacetimes. We describe
the basic geometric properties of such surfaces and their relationship to
slice-reducible Killing tensors, illustrating all concepts with a number of
examples. Massive particle surfaces have potential applications in the context
of uniqueness theorems, Penrose inequalities, integrability, and the
description of black-hole shadows in streams of massive charged particles or
photons in a medium with an effective mass and charge.
