Maximal extension of the Schwarzschild metric: From Painlevé–Gullstrand to Kruskal–Szekeres

It is shown that one can link in a continuous manner the Painlevé–Gullstrand partial extension to Kruskal–Szekeres maximal analytical extension, and thus exhibit of Schwarzschild metric unified picture. This done by finding coordinate system adopts two time coordinates, being proper congruence outgoing timelike geodesics, other ingoing both parametrized same energy per unit mass E. E range 1?E<?, with limit E=? yielding extension. So, through such an integrated description sees solution belongs this family extensions. different from Novikov–Lemaître also Novikov holding for 0<E<1 maximal, Lemaître 1?E<? partial, not moreover its evanescing Minkowski spacetime or inflating into Kasner spacetime, rather than ending spacetime.