The smeared-horizon observer of a black hole

A class of observers is introduced that interpolate smoothly between the Schwarzschild observer, stable at spatial infinity, and the Kerr-Schild observer, who falls into a black hole. For these observers the passing of the event and inner horizon takes a finite time, which diverges logarithmically when the interpolation parameter σ goes to zero. In the field theoretic approach to gravitation, the behavior at the horizons becomes regular, making the mass of the metric well defined.