flat universes. However  there is also an alternative interpretation when we restrict our attention to the thick-line rectangle of Fig.1. In fact  we realize that the upper tunnel (the strip where in the Reissner-Nordstr¨ om case we would expect to have the central singularity) is a copy of the lower tunnel. This suggests that we might identify the two tunnels. If we do that  the manifold becomes finite and cyclic in the timelike coordinate. In the extreme case M = M$_{0}$ the metric (2) becomes where φ is a differentiable and not vanishing function in the interval [0   ∞ ). In order to derive the maximal extension we shall follow the procedure adopted in [20]. To this purpose we consider the surface { ϑ = const   ϕ = const } and we write (28) as follows: By introducing null coordinates p and q defined as our metric becomes where now r is a function of p and q . It is worth mentioning that the surface { r = r$_{0}$  ϑ = const   ϕ = const } is made of radial null geodesics corresponding to lines parallel to p = const and q = const in the ( p  q )-plane. The metric (31) is regular for all real values of p and q . In order to understand where the coordinate singularity r$_{0}$ lies in the ( p  q )-plane we need to study the signs of φ ( r$_{0}$ ) and φ $^{′}$( r$_{0}$ ). First of all  notice that 13 φ ( r$_{0}$ ) = 1 2 g ′′ $_{00}$( r$_{0}$ )   φ $^{′}$( r$_{0}$ ) = 1 6 g ′′′ $_{00}$( r$_{0}$ ) ds 2 = ( r − r$_{0}$ ) $^{2}$φ ( r ) dp dq − r $^{2}$dϑ2 − r $^{2}$sin2 ϑ dϕ 2 (31) r ∗ := ∫ dr ( r − r$_{0}$ ) $^{2}$φ ( r ) = − 1 ( r − r$_{0}$ ) φ ( r$_{0}$ ) − φ $^{′}$( r$_{0}$ ) φ $^{2}$( r$_{0}$ ) ln ( r − r$_{0}$ ) + O ( r − r$_{0}$ ) (30) p := t + r $^{∗}$  q := t − r $^{∗}$  ds 2 = ( r − r$_{0}$ ) $^{2}$φ ( r ) [ dt − dr ( r − r$_{0}$ ) $^{2}$φ ( r ) ] [ dt + dr ( r − r$_{0}$ ) $^{2}$φ ( r ) ] (29) ds 2 = ( r − r$_{0}$ ) $^{2}$φ ( r ) dt 2 − dr 2 ( r − r$_{0}$ ) $^{2}$φ ( r ) − r $^{2}$dϑ2 − r $^{2}$sin2 ϑ dϕ 2 (28) VI. THE EXTREME CASE