  Starting from the Frolov-Zel'nikov stress-energy tensor of quantum massive
fields in the Schwarzschild background, we recover the contribution $S_{q}$ of
these field into the entropy of a black hole. For fermions with the spin
$%s=1/2$ $S_{q}>0$, for scalar fields $S_{q}>0$ provided the coupling parameter
is restricted to some interval, and $S_{q}<0$ for vector fields. The appearance
of negative values of $S_{q}$ is attributed to the fact that in the situation
under discussion there are no real quanta to contribute to the entropy, so
$S_{q}$ is due to vacuum polarization entirely and has nothing to do with the
statistical-mechanical entropy. We also consider the spacetime with an
acceleration horizon - the Bertotti-Robison spacetime - and show that $S_{q}=0$
for massive fields similarly to what was proved earlier for massless fields.
