  The (zeroth-order) energy of a particle in the background of a black hole is
given by Carter's integrals. However, exact calculations of a particle's {\it
self-energy} (first-order corrections) are still beyond our present reach in
many situations. In this paper we use Hawking's area theorem in order to derive
bounds on the self-energy of a particle in the vicinity of a black hole.
Furthermore, we show that self-energy corrections {\it must} be taken into
account in order to guarantee the validity of Penrose cosmic censorship
conjecture.
