https://youtu.be/eNhJY-R3Gwg?feature=shared
General Relativity makes two core statements about gravity:
Spacetime can’t be curved in any particular way.
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Locally spacetime adheres to the Equivalence Principle which states that locally curved spacetime is indistinguishable from an inertial frame of reference.
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Explicity this means that locally, curved spacetime follows the geometry of flat, Minkowksi spacetime (i.e. a local inertial frame can always be found at every point in curved spacetime). In flat spacetime the phenomenon of constant speed of light ($c$), length contraction and time dilation, and relativistic velocity addition would hold.
This also implies that a uniform gravitational field would be indistinguishable from a uniform accelerating non-inertial frame. By analogy this is like how the curved surface of the Earth appears flat locally to humans on this surface but as we “zoom” out the curvature from flatness becomes more noticeable.
Gravity is a result of curved spacetime.
The underlying principles that lead to this are
The geodesics for someone in freefall on the curved spacetime of the gravitational well created by Earth’s mass would be a path towards the center of the Earth. So if there was no Earth in the way and you where sitting in this gravitational well under the influence of no forces, you would follow a geodesic path towards the center of the well. However, Earth’s surface prevents us from following the geodesic path and being in freefall. When an object is not following its geodesic that means its being accelerated. So the Earth’s surface, which is preventing us from following our freefall motion, is thus accelerating us upward by 9.81 meters per second squared which is equivalent to the idea that we are accelerating downward 9.81 meters per second squared towards the Earth’s surface.
We can also think about this from the time dilation view. Consider an object under no forces in the spacetime of a gravitational well. Here clocks deeper in a gravitational well are slower than clocks farther from the center of the well. At the top of the object time passes faster than at the bottom of the object due to this time dilation. We might expect the object to stay at the same height with time. So this would be a straight line in a radius versus time diagram. However the different flow of time, means the top gets ahead of the bottom, which will ultimately cause the four-velocity (the velocity of an object in spacetime, tangent to its trajectory in spacetime) to turn towards Earth and decrease its radius. This is gravity!