  We assumed a stress tensor is necessary on the event horizon of a
Schwarzschild black hole or on the Rindler horizon for the Israel matching
conditions to be satisfied. We found the surface energy density $\rho_{s}$ is
vanishing but the surface pressure $p_{s}$ equals $1/16\pi l$ in both cases,
where $l$ is the proper distance from the horizon. The junction relations are
applied both for $r =$ const. and $T =$ const. surfaces, with the same results
for the surface parameters $\rho_{s}$ and $p_{s}$. We emphasize the nonstatic
feature of the spacetimes beyond the corresponding horizons.
