General Relativity is constructed with a Strong Equivalence Principle in mind.A strong equivalence principle can be formulated as follows:
at each point in spacetime in an arbitrary gravitational field, you can choose a "locally inertial coordinate system", such as
that in a sufficiently small neighborhood of the point under consideration, the laws of nature will have the same form as in the nonaccelerated Cartesian coordinate systems of SRT,
where "laws of nature" means all the laws of nature.
And what about the Mach principle? Mach himself gives an example in which two massive balls rotating relative to each other will not move away from each other under
by the action of centrifugal force, if there are no other bodies in the universe.
That is, the Mach principle also speaks about the nature of rotational motion.
And what is the basic law of rotational motion? This Is The Law Of Conservation Of Angular Momentum. Let's look at how Galileo and
change in spacetime
In Einstein's spacetime, the units of energy, momentum, and angular momentum are

Galileo Spacetime 
Einstein's Spacetime 
unit of pulse measurement kg * m/s 
not change 
not change 
the unit of energy, the Joule 
not change 
not change 
the unit of measurement of the angular momentum, Joule*s 
not change 
changes in direct proportion to the change in the second 
From this table, it can be seen that in Einstein's curved spacetime, the Law of Conservation of Angular Momentum must be written differently than in Galileo's spacetime.
Thus, the Law of Conservation of Angular Momentum is where the Strong Equivalence Principle comes into conflict with the Mach principle.
My proposed correction of the GR equation essentially means abandoning the Strong Equivalence Principle in favor of the Mach Principle.
Note that this does not require abandoning the Equivalence Principle entirely. Since the Weak Principle differs in that the words "laws of nature" are replaced in it
the words "laws of motion of freefalling particles". The weak principle is nothing more than another formulation of the observed equality of gravitational and inert masses,
while the strong principle is a generalization of observations of the influence of gravity on any physical objects.
And what do astronomical observations say about the fulfillment of the Law of Conservation of Angular Momentum in the Universe?
If we look at the angular momentum of galaxies, we can see that they are abnormally large, for example, our Milky Way galaxy
The angular momentum is equal to a huge number of 10 ^ 67 Joules per second. How can this be, because if the Strong Equivalence Principle were true
then it should have been so from the initial moment of the formation of the galaxy. But this can easily be explained by the fact that in the process of expansion of the universe
there is a decrease in its gravitational potential, which means a devaluation of the meter and second, and the angular momentum of all rotating bodies in the universe
increases in inverse proportion to the decrease in the meter.
This hypothesis of Yanchilin about the origin of the huge angular momentum of the rotation of galaxies can be verified by observations, for this it is necessary to build a graph,
similar to the Hubble graph. The abscissa axis also shows the distance to the galaxies, and the ordinate axis shows their angular momentum.
And if there is a tendency to decrease the angular momentum with increasing distance, the hypothesis will be confirmed. And it will also be proved that
that the Mach principle is true, and not the Strong Equivalence Principle.
By the way, from the fact that closer to a massive body, the angular momentum of other rotating bodies decreases, it follows that the Mach principle should be expanded by 180 degrees.
Mach said that if we spin on our axis, but there are no other bodies in the universe, how do we know that we are spinning?
The answer to this question turns out to be hideously simple. If there are no other bodies in the universe, then we simply will not be able to rotate around our axis, since our mass and moment
the inertia will become infinitely large.
Albert Einstein, at the time of the creation of the general theory of relativity, hoped that the Mach principle would find its embodiment in his theory.
Here is what he wrote at the time"...in the sequential theory of relativity, one cannot determine inertia with respect to 'space', but one can determine the inertia of the masses with respect to each other.
Therefore, if I remove any mass at a sufficiently large distance from all the other masses of the universe, then the inertia of this mass should tend to zero. "
On the contrary, the inertia of this mass will rush to infinity and we will simply lose the ability to move, both rotationally and translationally.
We are able to move and rotate thanks to the gravity of all other bodies in the universe.