The smeared-horizon observer of a black hole

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 σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} 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.