The paper is organized as follows. In section II we will discuss the singularities of the met- ric which emerge in the framework of noncommutative geometry when a point-like structure is smeared by the so-called Gaussian prescription. Section III treats the new transformation of the Schwarzschild coordinates which leads to the maximal atlas. Section IV continues these considerations and discusses the determination of the constants in the transformation. Section V interprets the results in terms of a Penrose diagram. Section VI is devoted to the extreme case where the mass is equal to a critical mass. In section VII we draw our conclusions. The replacement of the sharp point-like structure discussed above suggests that the metric can be based on the Gaussian mass distribution, The ansatz of an anisotropic perfect fluid energy-momentum tensor taken together with two equations of state in which the pressure is determined by the Tolman-Oppenheimer- Volkov equation leads to the noncommutative geometry inspired Schwarzschild solution [7] given by where M is the mass of the black hole, θ > 0 is a parameter encoding noncommutativity and γ is the incomplete lower gamma function. The singularities of the metric are determined by the equation According to [7] there are three possible scenarios, namely A striking feature of the metric (2) is the absence of a true singularity at r = 0. Moreover, the above classification is of numerical nature since the equation g$_{00}$ ( r ) = 0 cannot be solved 3 1. if M < M$_{0}$ ≈ 1 . $_{9}$√$_{θ}$$_{, the function}$ g$_{00}$ never vanishes, 2. if M = M$_{0}$ , g$_{00}$ vanishes just at one value r$_{0}$ ≈ 3 . $_{0}$√$_{θ}$ (extremal black hole), 3. if M > M$_{0}$ , there exist r ± with 0 < r − < r$_{+}$ such that g$_{00}$ ( r ± ) = 0 g$_{00}$ ( r ) := 1 − 4 M √$_{πr}$ γ ( 3 2 , r 2 4 θ ) = 0 . (3) ds 2 = ( 1 − 4 M √$_{πr}$ γ ( 3 2 , r 2 4 θ )) dt $^{2}$− ( 1 − 4 M √$_{πr}$ γ ( 3 2 , r 2 4 θ )) − 1 dr $^{2}$− r $^{2}$dϑ$^{2}$− r $^{2}$sin$^{2}$ϑ dϕ$^{2}$, (2) ρ$_{θ}$ ( r ) = M (4 πθ ) 3 / 2 e − r $^{2}$/ (4 θ $^{)}$. (1) II. SINGULARITIES OF THE METRIC