Аннотация:We consider a space-time of a spherically symmetric black hole with one simplehorizon. As a standard coordinate frame fails in its vicinity, this requires continuationacross the horizon and constructing frames which are regular there. Up to now,several standard frames of such a kind are known. It was shown in literature before,how some of them can be united in one picture as different limits of a generalscheme. However, some types of frames (the Kruskal-Szekeres and Lemaˆıtre ones)and transformations to them from the original one remained completely disjoint.We show that the Kruskal-Szekeres and Lemaˆıtre frames stem from the same root.Overall, our approach in some sense completes the procedure and gives the mostgeneral scheme. We relate the parameter of transformation e0 to the specific energyof fiducial observers and show that in the limit e_0 → 0 a homogeneous metric underthe horizon can be obtained by a smooth limiting transition