I posted it in SR/GR but probably it really belongs here: I can explain my motivation. Non red-shifted Hawking radiation is very intense. So when observer approaches the singularity, singularity is always hidden behind the apparent horizon. However, the horizon it covered with a cloud of hawking particles. These particles (in a frame of a falling observer) are emitted from the horizon but then fall back into the singularity together with the observer. But the singularity of mass M is represented with the mass of the matter inside the apparent horizon S and the 'cloud' C, M=S+C While C is almost negligible far from the singularity, it is quite possible that C>S close to it. But then singularity itself does not exist because the cloud 'blurs' the singularity and flattens space-time.