You have to dive in thougths to start thinking why rotations are exceptional. Every day we see things moving, in moviment we have 2 types: translations and rotations. What is especial abouth the second? Give it a try, it's possible to rotate only with translations? Yes, around another object it's possible, but around the object itself, no.
Rotations and translations are independent, they exist like a fundamental particles, like eletrons and neutrinos. Rotations can be decomposed in translations (the thing rotating must have some dimension) but translations can't be decomposed in rotations. Before you ask: "There is something with no dimensions which rotattes?" Yes, eletrons. They don't have a length, but they rotate, and we can even measure it with a property called spin. How can a point rotate? Is't not easy to interpretate this. If you ask to a physicist what is the interpretation of the spin, you'll enjoy the show, because there's no correspondence in reality to make analogies. The problem keeps going more difficult when you remember the fact that electrons can be waves too. So, here we go: how it's possible to tridimensional waves rotate? Better: the waves are, in fact, probability distributions, so you have a probability function sppining. Remember the spin property citted? They are not described by a 3D rotation, it's represented by a number called quaternion, a number with 4 dimensions, three complex and one real: q = 1+ai+bj+ck, and i² = j² = k² = 1. So, take a breath, now imagine it: the spin of an eletron is a measure of probabilities rotating in 4D space...
There's nothing in reality wich find correspondence with that. It's a inteligent answer to give to someone asking what is spin. If the physicist don't tell you that, he will start doing some funny malabarism, like saying "It's like a rotation, but it's not rotating, because there's nothing to rotate". Physicist are awsome people because they eat thougths like that in the breakfast, mathematicians also have this ability to think in things that don't exists, that can't even be imagined (like the Klein's bottle).
But there's more abouth rotations to blow your mind, Newton was one of the guys wich knew that. I'll describe he's famous mental experiment with a bucket of water to. Supose you have a bucket supended by a rope, and it's filled with water. Then, you start to twist the rope, in order to make the bucket rotate when you release it. With the water stationary, it's superficie is flat. After the bucket start rotating, the water will form a paraboloid, a concave shape. What makes the water acts like that? The centrifugal force, you'll say, but what is the origin of that force? Ask yourself, if you keep the bucket static and rotates all the universe around it, would that force appears again? In other words: is the centrifugal force relative to all the rest of the universe?
Did not understand? Perfectly, you are here to test your abstraction capacity. I'll use translations to explain, wich are intuitive to understand. Imagine someone passing fast througth your view and screaming. You'll feel the Doppler effect, but if that person is screaming static and you pass rapidly, you'll feel the Doppler effect exactly the same way. The same is true to eletric and magnetic filds. If you are holding a wire and someone comes very fast with a huge magnet, you'll feel an electrical current in the wire. If we invert, now you are running with a wire in hands, and someone is static with a magnet, the effects should be the same, rigth? You'll still feel the eletric corrent. So, is the same true to rotations? How do you change the perspective of a rotation? When you rotates something abouth it's own center, the thing is moving relative to all the rest of the universe, so the only way to invert it is rotatting all the universe in the opossity way.
Let me guess, you think this is a nonsense question? It is not. Ernest Mach (wich gives names to velocites like mach 1, mach 2) was a important physicits who seriously thougth abouth it [1]. He belived that all forces are relative, so when a object rotates, the centrifugal force comes from a relation between the object mass and the mass of very far stars (the significant part of the rest of the universe). In the other hand, Newton belived that when something is rotating, that object defines a ultimate center, and all the universe rotates around it. Ernest dit not like that interpretation, because the ideia of an absolute center it's regected by general relativity, and it gives a special importance to our position on the universe. Newton first tougth abouth this ideia when reflecting abouth the consequences of rotation on Earth, the oblatness shape of our planet is a original prediction of his theory. Well, Einstein and others supported Ernest, because he was an important name to them, so now you know that the question is important.
Back to the perspective of the bucket, if all the universe is rotating, we should get the same centrifugal force on the water just by rotating all the universe in the oposite way. Otherwise, the symmetry will be broken, and in physics symmetrys are very important. Well, antecipating the answer: we don't know if it realy occurs. Any experiment proposed to prove that should focus on the measure of a constant relating both objects, but such constant would be absurdly small, because the mass of the universe it's juts to big compared with any object. To understand that think in the constant of gravitation G, it measures exactly the force between two masses of 1 Kg separated by 1 meter. The constant involving the centrifugal force would be proportional to the ratio between the mass of a object and the mass of the observable universe. We can, actually, calculate the theoretical value of that constant, because we know approximately the mass and size of the observable universe, but to measure, it's just impossible, the magnitute of the constant is something like 10^(-70).
The experiment to measure it would also involve absurd things, like a hollow planet rotating. We know that inside a spherial shell the gravitation is null. But what if put that hollow planet to rotate? If something like a antigravitational field surge in it's interior, them it would be a evidence that rotations, indeed, causes a force relative to all the rest of the universe.
And how abouth rotating black holes?
Rotations in black holes are fabolous things to think abouth. When they rotate (every object on space is rotating), a region called "Ergosphere" is created, the analogous of Earth oblatness. But here, the space-time is being torn. Again, there's nothing in reality which finds correspondence with that, i'ts a new region of space to us. Thanks to math, we can describe it. The calculations showns that it's even possible to extract energy from there (thereby, also mass). And the coolest thing is that the region it's not beyond the event horizon, is acessible to us. Roger Penrose, another friend of Einstein, was one wich proved that. The region is permanently moving, dragging space-time around the black-hole. Here is a simulation on wikipedia wich shows an object entering the Ergosphere:
The object were going to rotate the black hole in the clockwise way, and just altered it's trajectory to anticlockwise, this is impossibly in Newtons Theory. Look at t, is the time in our referencial, t' is the time to the object. Like in the film Interestelar, the time just exploded for the object, to us the simulation ocurs on 69 seconds, to the object, almost three hours passed (9900 seconds)!
After enthering the Ergosphere the trajectory of the object is dragged, it becomes something like a gif with several images, it's like seeing different frames of time distributed in space! Now you can have a lot of fun imaging that!
Thanks for the reading
Here is an magnificent article (in portugues) abouth interpretations on the gravitational force:[1]https://www.scielo.br/scielo.php?pid=S1806-11172019000300701&script=sci_arttext
