The smeared-horizon observer of a black hole

TL;DR

This paper introduces a new class of black hole observers that smoothly interpolate between known types, revealing finite horizon crossing times and regularized horizon behavior in field theory.

Contribution

It defines a novel observer class that bridges Schwarzschild and Kerr-Schild observers, providing insights into horizon crossing and regularization in gravitation theory.

Findings

Finite horizon crossing time for these observers.

Divergence of crossing time as interpolation parameter approaches zero.

Regularized horizon behavior in the field theoretic approach.

Abstract

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 $\sigma$ 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.