  In this article, we study the trajectory equations of the bounded radial
geodesics in the generalized black-to-white hole bounce with mass difference
and the Schwarzschild-to-de Sitter transition approximated by the thin-shell
formalism. We first review the trajectories equations of the general radial
geodesics in Kruskal-Szekeres (like) coordinates of the Schwarzschild and de
Sitter spacetimes, respectively. We then demonstrate how one relates the radial
geodesics on each side of the shell by correctly choosing the constants of
integration after performing the two coordinate transformations mentioned in
our previous work, arXiv:2302.04923. We next show that the coordinate system
used in the resulting Penrose diagram has no illness at the thin shell but
instead creates a degeneracy between the timelike geodesics and null geodesics
at the event horizons where the second transformation is applied. Due to this
problem, we conclude that a global conformal coordinate chart for the spacetime
connected via a static spacelike thin shell in general does not exist, except
for some special cases. Since this is an extension of our work,
arXiv:2302.04923, we focus on Schwarzschild and de Sitter spacetimes, though
the method should be applicable to any cut-and-pasted spacetime connected with
a static spacelike thin shell.
