In Kruskal coordinates, a change of coordinates provides a nonvanishing metric for 
.The topology of the transformed metric consists of two sheets joined by a branch point. The new coordinates are called the Kruskal-Szekeres coordinates by Misner et al. (1973)
where T is an arbitrary constant. The Schwarzschild metric then becomes
(Weinberg 1972, p. 208). Shapiro and Teukolsky (1983, p. 353) define it slightly differently by
so that
.The topology of the transformed metric consists of two sheets joined by a branch point. The new coordinates are called the Kruskal-Szekeres coordinates by Misner et al. (1973)(1)
(2)
where T is an arbitrary constant. The Schwarzschild metric then becomes
(2)
(Weinberg 1972, p. 208). Shapiro and Teukolsky (1983, p. 353) define it slightly differently by
(4)
(5)
so that
(6)
(7)
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