content_image/347918.jpg content_image/347917.jpg content_image/347914.jpg content_image/347915.jpg content_image/347916.jpg content_image/347913.jpg content_image/347912.jpg
r$_{+}$ , namely 

with 

<img src='content_image/347918.jpg'>

<img src='content_image/347917.jpg'>

On the other hand the expansions of the tortoise coordinate r ∗ and of the functions e ± 2 γr$_{∗}$ are 

Hence, we have 

<img src='content_image/347914.jpg'>

<img src='content_image/347915.jpg'>

<img src='content_image/347916.jpg'>

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 

<img src='content_image/347913.jpg'>

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 

<img src='content_image/347912.jpg'>

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. 

## V. RADIAL OBSERVERS 

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$_{+}$ 

