black hole tidal forces

Suppose we drop an astronaut into a black hole, feet first.
since the feet are closer to the singularity’s gravity, the feet feel a stronger tug than the head, and is pulled more strongly. The astronaut is theoretically stretched out of shape…an effect refferred to as “Spagettification”.

From the head’s point of view, the singularity is pulling at the feet.

But…from the feet’s point of view, something is pulling at the head.

what is this anti-gravitational force?

It’s just inertia. The head just lags behind because it is not as close to the source of the gravity. So from the feet’s point of view, the force causing the head to be yanked away from it is a relative lack of gravitational attraction.

I suppose a loose analogy could be made to a hot air balloon. It’s not anti-grav that causes it to yank up on the basked, it’s the fact that gravity is acting much less on the contents of the balloon than on the cold/dense air around it. Or rather, there is less air in a cubic foot of balloon than a cubic foot of outside air.

Basically, the anti-gravity force is simply “weaker gravity”. It’s not that the head is being “pulled away” (even if the feet - ignoring the simple fact that feet aren’t conscious - may percieve it that way), it’s just that it’s “not being pushed fast enough”.

Then again, I think the astronaut (and his feet) will be too busy having his life (or his boots) flash before his eyes to think about “Spagettification”. But maybe this astronaut is Aristotle or something… “Hmm… I’m about to be sucked into a quantum singularity… I wonder what my feet are thinking right now.”

Newton’s Third Law: “For every action, there is an equal and opposite reaction.”

I should’ve made myself clearer. I think what you are refering to is just the action and reaction forces.