[Pmb]

In Relativity there is no difference between what appears to happen and what does happen.

That’s incorrect. There is a clear distinction between what is observed and what is reckoned. E.g. when an object is approaching us there are two effects going on which determine what we ‘see’ and what we ‘reckon’– The former is defined according to what is observer actually sees with nothing taken into account while the second is defined according to what we know to be the case by both calculation and observation. For example; when an object approaches us then we see things happening faster than what we know to be true. The Doppler effect causes this. The second is what we know to be the case from what theory tells us. I.e. what is the rate that photon emitter is emitting photons when we account for Doppler shift. That’s why in the authors of the text Exploring Black Holes uses the term reckon for what actually happens as opposed to what appears to happen.

E.g. see how the term reckon is used here
http://astro.cornell.edu/academics/courses/a290/lectures/A2290_36%20(Free%20Fall).pdf

Clocks in motion or under acceleration (or gravity) not only appear to slow, they really do. Objects in motion or acceleration don't merely appear to shrink, they really do. Obj

But they appear to run slow for two reasons, (1) time dilation and (2) Doppler effect. If time dilation didn’t exist in nature then the rates at which moving clocks run would still appear to run at a rate which would depend on (1) the speed of the object and (2) the direction the object is moving in.

Etc.

[spartaman64]

The event horizon and the singularity are two different things. The event horizon is when light can no longer escape the black hole's gravity and the singularity is theoretically an point in the center of infinite destiny and is infinitely small. it is still theoretical though.