  In recent work on black hole entropy in non-perturbative quantum gravity, an
action for the black hole sector of the phase space is introduced and
(partially) quantized. We give a number of observations on this and related
works. In particular we show that (I) the entropy calculation applies without
change to generally covariant theories having no black hole solutions, (II) the
phase space constraint used to select the black hole sector is not the apparent
horizon equation, which is the natural phase space constraint separating
trapped and untrapped regions on an initial data surface, and (III) there
appears to be at least one other phase space constraint which leads to the
conclusion that the entropy associated with a bounding two-dimensional surface
is proportional to its area.
