I read on the mathematic constraints as we solve Einstein’s field eqs. for the Schwarzschild metric, and they are the signature of the matrix and the sign of the determinant. Thus we are free to choose a (-) sign for the first two metric terms, those for time and radius, on the inside of the event horizon !!! The metric quantity S= 1-2m/r is here zero, and by choosing a (-) going inward, the asymptote of 1/S is now symmetric, coming back down the pole. THIS IS A SUPERIOR FORM. We will no longer have to mumble things like “timelike intervals are spacelike and vice versa”.
I have been looking at integration of proper distance… quite a dance, and my choice of sign constitutes am algebraic ‘switch’. goes from + to – across an event horizon. Thinking now separately of the Kerr solution, GR seems to like math ‘switches’.