Horizon pressure from junction conditions for Schwarzschild and Rindler geometries

Abstract

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.