11. General Relativity and the Law of Conservation of Energy.
Let two bodies with masses m1 and m2 be at a distance r. Then the gravitational energy of their bond is equal to
Now let's assume that these two bodies approached a very massive body, so that time slowed down by half.
This will mean that in the Einstein coordinate system, the distance between them will also be reduced by half, since the meter
in the SI system, this is the length of the path traversed by light in a vacuum over a time interval of 1/299,792,458 seconds, hence,
the meter will double and the apparent distance between the two bodies will decrease by half.
But this, in turn, will mean that the gravitational binding energy of these two bodies will double.
And this is a violation of the law of conservation of energy.
Is this why the so-called "dark energy" is needed to explain the expansion of the universe?
And if we take into account that the gravitational constant G changes inversely with the deceleration
in this case, the gravitational energy of the connection of these two bodies will remain unchanged and, the law of conservation
energy will be respected.
Thus, the elimination of this error returns the Law of Conservation of Energy to cosmology, and "dark energy"
to explain the expansion of the universe, it is not necessary. "Dark energy" is the same consequence of an error in the GR equation
so are black holes.