  A modified version of the Schwarzschild geometry is proposed. The source of
curvature comes from an anisotropic fluid with $p_{r} = -\rho$ and fluctuating
tangential pressures. The event horizon has zero surface gravity but the
invariant acceleration of a static observer is finite there. The Tolman - Komar
energy of the gravitational fluid changes sign on the horizon, equals the black
hole mass at infinity and is vanishing at $r = 0$. There is a nonzero surface
stress tensor on the horizon due to a jump of the extrinsic curvature.
Near-horizon geometry resembles the Robinson - Bertotti metric and not the
Rindler metric which corresponds to the standard Schwarzschild spacetime. The
modified metric has no signature flip when the horizon is crossed and all
physical parameters are finite throughout the spacetime.
