Regular Frames for Spherically Symmetric Black Holes Revisited

We consider a space-time of spherically symmetric black hole with one simple horizon. As standard coordinate frame fails in its vicinity, this requires continuation across the horizon and constructing frames which are regular there. Up to now, several such kind known. It was shown literature before, how some them can be united picture as different limits general scheme. However, types (the Kruskal–Szekeres Lemaître ones) transformations from original remained completely disjoint. show that stem same root. Overall, our approach sense completes procedure gives most relate parameter transformation e0 specific energy fiducial observers limit e0→0, homogeneous metric under obtained by smooth limiting transition.