  This paper is devoted to the study of the statistical mechanics of trapped
gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a
consequence, a discrete spectrum dependent on the Legendre index $\ell$ similar
to the harmonic oscillator one is obtained and a statistical study is
performed. The mean energy $<E>$ results as a sum of two discrete Planck
distributions with different dependent frequencies. As an important
application, we derive the semiclassical Bekenstein-Hawking entropy formula for
a static Schwarzschild black hole by only requiring that the black hole
internal energy $U$ is provided by its ADM rest energy, without invoking
particular quantum gravity theories. This seriously suggests that the interior
of a black hole can be composed of trapped gravitons at a thermodynamical
temperature proportional by a factor $\simeq 2$ to the horizon temperature
$T_h$.
