but has still not crossed the second horizon at r − , the radial coordinate r becomes timelike, implying that the motion proceeds with decreasing r . Once the observer has crossed the Cauchy horizon at r − , the coordinate r becomes spacelike again. This means that we have two possible kinds of motion given by increasing and decreasing values of r . At this point the observer can take two decisions: either to cross the timelike surface r = 0 in order to approach an asymptotically flat region or to reverse his/her course as is the case in the Reissner-Nordstr¨ om metric [18]. By taking the latter decision, the observer will cross another copy of the surface r = r − . Having entered the new region r − < r < r$_{+}$ the radial coordinate becomes again timelike and the observer is forced to cross a new copy of the event horizon r$_{+}$ . In this way the observer will emerge out of a white hole in an asymptotically flat universe. However, the journey of the observer might not finish here since he still has the possibility to enter the noncommutative inspired Schwarzschild black hole living in this new universe. The result is the possibility to make a trip through an infinite number of universes connected by black hole tunnels. In order to depict the dynamics described above we shall construct a Penrose diagram (see Fig. 1) for the spacetime structure of the maximal extended Schwarzschild solution inspired by noncommutative geometry. First of all, we observe that the radial null geodesics in the metric (9) are du/dv = ± 1. For this reason it is convenient to switch to null coordinates p = u + v , q = u − v with v = e γ + r$_{∗}$ sinh ( γ$_{+}$t ) and u = e γ + r$_{∗}$ cosh ( γ$_{+}$t ) in order to apply the so-called Penrose transformation P = tanh p and Q = tanh q . It is clear from (27) that the equation of the apparent singularity at r$_{+}$ reads u 2 − v 2 = 0. Thus, in the ( Q, P )-plane the equation u = v becomes Q = 0 whereas u = − v reads P = 0. Moreover, the null infinities p = ±∞ and q = ±∞ are mapped into P = ± 1 and Q = ± 1. In this way we mapped the ( v, u )-plane in the square [ − 1 , 1] × [ − 1 , 1] where as usual we can introduce new coordinates U = ( P + Q ) / 2 and V = ( P − Q ) / 2. We recall that the coordinate singularity at r$_{+}$ has equation U = ± V . The null infinities are now straight line segments with equations U + V = P = ± 1 and U − V = Q = ± 1, while the lines r =const in the subspace { ϑ = const , ϕ = const } which are represented by the hyperbolae u 2 − v 2 =const are still hyperbolae in the ( U, V )-plane with equation [19] Concerning the regions r < r$_{+}$ we just repeat the above procedure with v = e γ$_{−}$r$_{∗}$ sinh ( γ − t ) 11 α 2 [( U + 1 α ) 2 − V 2 ] = 1 , α := 1 − C 1 + C , C := e 2 pq = const .