Inside a Black Hole: Rest Frame & Singularity

[tionis]

Once I cross the event horizon of a BH, is it valid to say that I'm at rest and the singularity comes up to meet me?

 

[rootone]

The fact of having crossed the event horizon makes no difference other than that from there you can only go deeper into the black hole.
At some time in the fairly near future you will inevitably encounter whatever the singularity is.
You can consider your self to be moving (which makes sense because you considered yourself to be moving before you got to the horizon.),
or you can consider that center of the black hole is moving towards you, which is equally valid.
However there is no good reason why crossing the horizon implies a need to switch to a different frame of reference.

 

[Nugatory]

Once I cross the event horizon of a BH, is it valid to say that I'm at rest and the singularity comes up to meet me?

No.
If you are in freefall, then it is always valid to consider yourself at rest and this works both inside and outside the horizon. However, once inside the horizon there is no way of thinking about the singularity approaching you, or looking towards it or away from it, or being a greater or lesser distance from it. The singularity is in your future, the same way that on Sunday night Monday morning is in your future.

 

[Dale]

Once I cross the event horizon of a BH, is it valid to say that I'm at rest and the singularity comes up to meet me?

The singularity is a moment in time, not a location in space. It would be a little strange to say "Friday comes up to meet me".

Edit: what Nugatory said

 

[tionis]

It is a moment in time, true, but we assign this moment in time shapes, like a ring, and spaghettification powers etc. I still don't understand how a moment in time can have all those attributes.

 

[PeterDonis]

we assign this moment in time shapes, like a ring, and spaghettification powers etc.

Those properties aren't assigned to a moment in time. They are assigned to the spacetime geometry. (Actually, in Kerr spacetime, the ring singularity is timelike, not spacelike, so it isn't a moment of time anyway, it can be seen as a ring in space. But the ring by itself still doesn't have all the properties you are talking about; they are still properties of the spacetime geometry.)