At every spacetime point, there is a locally inertial frame in which the effect of gravitation is absent. Can this point be taken as the center of a black hole?

(the following is the final draft of the answer, followed by the original draft)

No, because ‘frames’ are an imaginary measuring construct in an attempt to describe a ceaseless ongoing process. And no, results from ‘the frame’, even if “proof-able”, do not describe the process as it progresses. What is gravity? What is inertia? What and why is particle interaction? These things. Spacetime is the worst phrase ever. Whoever thought that sloppy joe plop needs to have his “scientisting” license pulled. Time is exactly like ‘frames’. Time also is a human construct devised for scheduling and measuring. The concept of “Earthling time” means nothing outside of human endeavor. All those measurements made using Earth time under Earth conditions don’t really cover all the variables, because half the variables are unknown. And you can’t see them “in frames” either. There is space (without”time”) - look out a window for proof … that’s space. But there’s no “time” outside that window because time is ‘made up’. Kind of even the scientific methods of “keeping time based on some basic universal function” - except it ISN’T universal - it’s local. (As usual we think we “see it all” just to find out we can’t see shit, and probably won’t figuring the lifespan of a species dominion on this planet over ‘time’ - they come and go - so shall we - probably before figuring out ‘the small stuff’.) Hence the concept of “singularity”. The catch-all be-all word that means absolutely nothing. It describes an assumed phenomena impossibly occurring in space (the place where all of us, even non-Earthlings, live. Singularity is used in those places where… “I just don’t know and haven’t a clue”. So, there’s a “singularity” at the heart of a black hole, is there? Well… that certainly explains that. You see, this doesn’t take into account that a black hole is a three dimensional object, a ≈sphere, in three dimensional space. Space, where we live; is three dimensional (3D). No more, no less. Space is made of particles (and waveforms) - even those big empty looking places are made of “small” particles and are filled with waveforms - (because there can never be “nothing”) … there are no “voids” in space. (but how can ‘round’ orbital trajectories fill cubical space, you ask? good question! Think about it a lot before asking it though.) Singularity. This word gets whipped out for the “in the beginning” nonsense, and it gets put in the middle of black holes, and they worry about ‘creating’ one in particle labs (only a moron would consider this possible, but there are plenty of morons), etc. If there’s an unknown process or two occurring at any state - you can bet your ass a “singularity” did it. Isn’t this attributed to Mr. Einstein’s work? He had a LOT of bad concepts to incorporate into reasonable speculation as to the nature of certain natural phenomena - I’m still impressed he did as well as he did. And then people go on and on to misinterpret him. The math WAS bad (but he was trying to express phenomena with ‘inadequate’ numbers and using incomplete, missing, misinterpreted, and “made up” data). So, you claim the point at the center of a black hole - where gravity (conceivably) cancels itself out when two centers of gravity overlap … is the center of a “ball” of mass (compressed matter) that has been pulled into the black hole … matter that is rendered smaller and smaller (friction, mechanical compression of orbital ‘clouds’). (true story by the way)… There is only one direction inside the event horizon, and that is ‘down’. You figure there’s no gravity there. In the “middle” particle, the center of gravity (CoG), eh? Interesting supposition. How do you go about verifying it’s possibility? Keep in mind CoG. If two objects [mass::matter::particle] WERE able to occupy the same space at the same time, which I’ve heard is pretty unlikely, but if an object the size of Earth WERE able to infall, stay atomically intact (I don’t know if that particle interaction could occur between two such disparaging complexities) ———→ this caused a conundrum I had to explore, sorry about the delay of several days. if they COULD overlay... That’s just it. They can’t. Well… I guess I didn’t have the answer after all. I’m sure another fine mind will come along citing Schwarzschild, Einstein, Fig Newton, and Mr. Fig. And fantastic