r$_{+}$ , namely with On the other hand the expansions of the tortoise coordinate r ∗ and of the functions e ± 2 γr$_{∗}$ are Hence, we have From Lemma 1 it follows that α can never vanish and we can choose γ so that the singularity at r$_{+}$ is cancelled. This happens if γ is chosen to be Clearly, it is not possible to cancel both singularities at once. In order to remove the singularity at r − we can proceed as we did above and we find that If we choose γ = γ$_{+}$ in the ( v, u ) coordinates we can proceed from an arbitrarily large r towards smaller r across the set r ∈ ( r − , r$_{+}$ . If we want to continue further across r = r − we have to go back to the coordinates ( v, u ) and choose γ = γ − . In this way we can continue across r = r − and reach r = 0 since it is not a singularity for the metric (2) and even continue through this timelike surface. We now analyze the motion of a radial observer inside the noncommutative geometry inspired Schwarzschild black hole. In doing so we will not address issues of stability which we postpone to a future investigation. When the observer enters the event horizon at r$_{+}$ 10 V. RADIAL OBSERVERS γ − = 1 2 g ′ $_{00}$( r − ) . γ$_{+}$ = α 2 = 1 2 g ′ $_{00}$( r$_{+}$ ) . g$_{00}$ ( r ) e 2 γr$_{∗}$ = ( r − r$_{+}$ ) ( α − 2 γ ) /α [ α + ( β + 2 βγ α ) ( r − r$_{+}$ ) 2 + O ( r − r$_{+}$ ) 2 ] . r ∗ ( r ) = 1 α ln ( r − r$_{+}$ ) − β α $_{2}$( r − r$_{+}$ ) + O ( r − r$_{+}$ ) $^{2}$, e ± 2 γr$_{∗}$ = ( r − r$_{+}$ ) 2 γ/α [ 1 ∓ 2 βγ α 2 ( r − r$_{+}$ ) + O ( r − r$_{+}$ ) 2 ] . α := g ′ $_{00}$( r$_{+}$ ) , β := 1 2 g ′′ $_{00}$( r$_{+}$ ) . g$_{00}$ ( r ) = α ( r − r$_{+}$ ) + β ( r − r$_{+}$ ) 2 + O ( r − r$_{+}$ ) 3