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We assumed a stress tensor is necessary on the event horizon of aSchwarzschild black hole or on the Rindler horizon for the Israel matchingconditions to be satisfied. We found the surface energy density $\rho_{s}$ isvanishing 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 areapplied both for $r =$ const. and $T =$ const. surfaces, with the same resultsfor the surface parameters $\rho_{s}$ and $p_{s}$. We emphasize the nonstaticfeature of the spacetimes beyond the corresponding horizons.

Horizon pressure from junction conditions for Schwarzschild and Rindler geometries