The nonsimultaneous nature of the Schwarzschild R=0 singularity

The relationship between the two well‐behaved coordinate systems of Lemaître–Tolman–Novikov, and Kruskal–Szekeres–Penrose indicates that the Schwarzschild R=0 singularity is intrinsically nonsimultaneous. It follows that the simultaneous synchronous coordinates of Wald and Yip do not exist on the complete Schwarzschild manifold. In the process, the coordinate transformations between the Schwarzschild exterior model in its various common coordinate systems and the vacuum Lemaître–Tolman model (which includes Novikov coordinates and the closed Kantowski–Sachs model) is derived. It is also shown that, contrary to statements in the literature, the closed Kantowski–Sachs model is well‐behaved limit of the Lemaître–Tolman model. © 1996 American Institute of Physics.