  Recently Bekenstein and Mayo conjectured an entropy bound for charged
rotating objects. On the basis of the No-Hair principle for black holes, they
speculate that this bound cannot be improved generically based on knowledge of
other ``quantum numbers'', e.g. baryon number, which may be borne by the
object. Here we take a first step in the proof of this conjecture. The proof
make use of a gedanken experiment in which a massive object endowed with a
scalar charge is lowered adiabatically towards a Schwarzschild's black hole and
than dropped into the black hole from some proper distance above the horizon.
Central to the proof is the intriguing fact that the self-energy of the
particle receives no contribution from the scalar charge. Thus the energy with
which the object is assimilated consists of its gravitational energy alone.
This of course agrees with the No-scalar-Hair principle for black holes: after
the object is assimilated into the black hole, any knowledge of the scalar
field properties is lost. Using the GSL, we reach the conclusion that the
original entropy bound was not improved by the knowledge of the scalar charge.
At the end we speculate on whether or not massive vector fields may serve in
the tightening of the entropy bound.
