12 - Wednesday

One can't really use a Kruskal mapping that keeps X as a function of the cosh of t and T the sinh of t everywhere. If you do, then you are restricted to working exclusively in the region -1<t<1 as otherwise mapping between Schwarzschild and Kruskal coordinates becomes singular.

\[t=4m\cdot\mathrm{arctanh}(\frac{T}{X})\]