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

Matching Radial Geodesics in Two Schwarzschild Spacetimes (e.g.  Black-to-White Hole Transition) or Schwarzschild and de Sitter Spacetimes  (e.g. Interior of a Non-singular Black Hole)