How can we feel the effects of a Black Hole if all the mass is gone? This question may help me learn more about the subtleties involved between the notions of gravity, in the Newtonian sense and those of curved spacetime, in the General Relativity sense.
I will take the risk that it may also show my lack of understanding of basic GR  concepts.
Unfortunately, any possible answers may be a matter of interpretation and/or opinion, as although GR has been confirmed in many ways, we are , as far as I know, lacking direct observational evidence of it's more exotic aspects, such as Black Holes.  
No offence intended, but personal opinions as to what is inside a black hole are not intended  as part of the question, I just want to stick to the question on a physical basis only.
My question is based on a comment by Kip Thorne, in essence, saying that "inside" a Black Hole is empty and that thinking there is crushed matter of any kind inside is an incorrect intuitive picture.
If the material that is the source of the black hole no longer exists, (gone to another universe, down a wormhole to another part of our universe,  or whatever, take your pick of possible outcomes), how can we still be affected by it, either  gravity wise or curved spacetime wise?
In other words, if the mass is gone, it's  gone, so how can we still feel the effects of it, unless time runs so slowly at the proposed event horizon that, for coordinate observers, it's effects are always felt?
EDIT What Thorne actually says is "the matter is gone, it's  completely destroyed, it no longer exists", Quantum Physics,  PBS NOVA on YouTube so


*

*Ernie's answer has validity, imo  and 

*It's a NOVA production, not a peer reviewed article in a generally accepted publication, it may be taken as a  broad popularisation. END EDIT
Apologies  if there is a duplicate somewhere on this site, I could not see one in the suggestions as I wrote this question.
 A: This is really Kip Thorne's interpretation of the black-hole collapse. Many other scientists and theorists would disagree and in many quantum gravities the interior of the black hole is not empty and the central singularity is somehow regularized. 
In any case, what you really feel pulling on you is not the mass very far away, what you really feel is the space-time configuration immediately around you. One patch of space-time does not really know whether there is some mass far away, it really curves only due to the matter-energy contained in it and due to the conditions on it's boundary. In this way, through boundary conditions of very small patches of space-time, the information about a matter source is "passed on" to very far away regions. 
But this also means that if you take a single point and "wrap" it around with some very extreme boundary condition, the space-time can warp and curve around it as if an infinite density of mass was there. Specifically, far away from such a "boundary point", you would not be able to tell whether the space-time is curved due to some star or due to this weird point. In this precise sense, theoretical physicists talk about black hole solutions as of "vacuum solutions" because there is no non-zero matter density anywhere in the space-time, only a singular point. 
But whether the matter is indeed "squeezed out" of the space-time leaving only a relict in the form of a space-time singularity or whether it is somehow "in the singularity" (and whether such a singularity even exists) is a matter of interpretation and controversy.
A: I think you may be referring to this interview: http://www.space.com/17086-bizarre-black-holes-kip-thorne-interview.html.  If not, possibly something of the same idea.
He didn't say that the inside of a black hole is empty.  He said that matter which falls into a black hole is destroyed.  When it's destroyed, its mass attribute becomes an energy attribute, and that energy resides in the warped space-time of the black hole.
The interior of the black hole may be empty of matter, but it has a rich energetic structure which is not completely understood.  As it's a singularity, it's difficult to compare it to other structures we know and understand.
