Regular Frames for Spherically Symmetric Black Holes Revisited

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

Automated summary

This study considers the spacetime of a spherically symmetric black hole with a simple horizon. Due to the failure of a standard coordinate frame near the horizon, continuation and construction of regular frames are required. It is shown that Kruskal-Szekeres and Lemaitre frames stem from the same root, providing a more general scheme.