  An anisotropic fluid with a negative radial pressure $p = - \rho$ is supposed
to exist near the horizon of a Schwarzschild black hole. The constant energy
density $\rho$ depends only on the black hole mass. The radial acceleration of
the static observers is constant but its modulus has exactly the Rindler form,
as was recently suggested by Dahia and Felix da Silva.
  The structure of the stress tensor is similar with that obtained previously
for the interior region of a black hole, excepting the time dependence.
