[puppypower (OP)]

In other discussion, the question was why does water at the equator, not flow to the poles and pool there, since the earth is wider at the equator and therefore the equator is at elevation relative to the poles. If you put the earth on its side the equator would look like a large hill. The consensus answer was the rotation of the earth causes the water to remain at the equator due to the centrifugal force sort of lifting the water against gravity, like rotating water in a glass will lift the water toward the walls where rational speed is highest.

Below is a diagram of the earth's gravitation profile. The gravity is higher the poles and lower at the equator and does corresponds to 0.35% difference that the centrifugal force causes at the equator due to the earth's rotation.



The question now becomes since the centrifugal force can alter the acceleration of gravity, a shown in the diagram, does it also alter space-time at the equator? Does General Relativity have a provision for the acceleration change due to rotation and the centrifugal force?

It sort of makes sense, since the rotation of the earth moves matter on a curved path, while GR is about the curvature of space, which also moves matter on a curved path. Does this common link make the centrifugal force part of GR?
 

[PmbPhy]

The question now becomes since the centrifugal force can alter the acceleration of gravity, a shown in the diagram, does it also alter space-time at the equator?

That's difficult to answer because "alter space-time" is a vague term. If by it you're asking if there is an associated spacetime curvature then no, there isn't.

Does General Relativity have a provision for the acceleration change due to rotation and the centrifugal force?

Also unclear. What does "have a provision" mean? In GR the centrifugal force is considered to be a gravitational force because it's an inertial force and in GR all gravitational forces are inertial forces and vice versa.

Einstein spoke of the both the centrifugal and Coriolis force in an article he published in Nature in the February 17, 1921 issue:

Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation.

[puppypower (OP)]

Since centrifugal force has the same impact as negative gravity; pushing mass outward away from the center of gravity, was the rotation of the earth induced by an exothermic output stemming from the loss of gravitational potential?

In other words, the other three forces of nature, when lowering potential, give off energy. This energy can be used to increase the same force potential elsewhere. For example, if an electrons drops one energy level in a hydrogen atom, that photon can be used to induce an electron to gain one energy level, elsewhere.

That being said, if gravity was a force, it should give off energy when lowering potential; such as the earth forming. This energy output would be partially reflected as an increase in local gravitational potential, negative gravity affect, such as created by centrifugal force. The result is an induced rotation until the centrifugal force matches the exothermic out.

Does rotation and revolutions of moons, planets, stars, solar systems, galaxies, etc., reflect the accumulative exothermic output of the entire galaxy, due to lower gravitational potential? The excess energy output will leave the galaxy and induce an antigravity affect in the universe; dark energy?


Another question is since the centrifugal force lowers the acceleration of gravity at the equator, relative to the poles, and gravity is connected to space-time via general relativity, what would be the implication of a space-time reference gradient on the surface of the earth, from pole to equator? It is sort of like having two twins aging differently, yet connected in ways that allows a dynamic equilibrium, but with a perpetual lag in time and space. 

[PmbPhy]

Since centrifugal force has the same impact as negative gravity; pushing mass outward away from the center of gravity, ...

Centrifugal force does not behave like negative gravity. For some reason you're assuming that the source of gravity is on the axis of rotation whereas in fact there is no source of gravity to inertial forces. However Mach argued that the sources of inertial forces are the distant stars and if one argues that there is a source to inertial forces then that's where the centrifugal force is pointing.

Whatever gave you the impression that inertial forces have a source or center of gravity?

That being said, if gravity was a force,...

I don't know where you heard otherwise but gravity is a force. In fact Einstein never said it was otherwise. He said that gravity is just like inertial forces and since the force of gravity is real then so too are inertial forces. People often get that backwards.

[evan_au]

was the rotation of the earth induced by an exothermic output stemming from the loss of gravitational potential?

Was there a loss of gravitational potential? Yes - there is less gravitational potential in a concentrated mass of matter than a uniformly distributed dust cloud.

Was it exothermic? Yes - the collision of those dust grains & meteorites made it get hot, and it gave off some of that heat as it cooled down to a solid crust. (More heat was added due to radioactive decay, so the high temperature of the core of the Earth is not entirely due to that early gravitational heating.)

Did this cause the rotation of the Earth? I would rather say that the rotation of the Earth reflects conservation of angular momentum, from the eddy in the protoplanetary disk that formed the Earth.