Israel coordinates for all static spherically symmetric spacetimes with vanishing second Ricci invariant

Static spherically symmetric spacetimes with a vanishing second Ricci invariant constitute an important class of solutions to Einstein's equations and more generally as archetypes of regular black holes. When studying completeness, one is most often presented with the Kruskal-Szekeres procedure. However, this procedure only works if the spacetime admits a single nondegenerate Killing horizon (a single bifurcation 2-sphere). Here, we generalize the Israel procedure to examine a constructive approach to completeness based entirely on the static spherically symmetric nature of spacetimes with a vanishing second Ricci invariant. It is shown by ``block gluing'' that the Israel procedure can cover two bifurcation 2-spheres but can fail with three. No coordinate transformations are used in this work.