A quasi-black hole, either non-extremal or extremal, can be broadly defined
as the limiting configuration of a body when its boundary approaches the body's
quasihorizon. We consider the mass contributions and the mass formula for a
static quasi-black hole. The analysis involves careful scrutiny of the surface
stresses when the limiting configuration is reached. It is shown that there
exists a strict correspondence between the mass formulas for quasi-black holes
and pure black holes. This perfect parallelism exists in spite of the
difference in derivation and meaning of the formulas in both cases. For
extremal quasi-black holes the finite surface stresses give zero contribution
to the total mass. This leads to a very special version of Abraham-Lorentz
electron in general relativity in which the total mass has pure electromagnetic
origin in spite of the presence of bare stresses.Comment: 22 page
