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I often read that a curvature in time (the rate at which clocks tick) near a massive object, is considered to be the source of Newtonian gravity.

This got me wondering, does General Relativity use the changing rate that clocks tick along the radial coordinate of a massive object to determine the rate of acceleration (gravitational acceleration) towards that object, and if not, then how exactly is a curvature in time being utilized to express what is considered to be Newtonian gravity?

Qmechanic
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4D Menu Systems
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    Related: https://physics.stackexchange.com/q/609217/123208 – PM 2Ring Dec 30 '23 at 22:46
  • This might help - A new way to visualize General Relativity – mmesser314 Dec 31 '23 at 00:06
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    “a curvature in time (the rate at which clocks tick)” - This is incorrect. The time dilation is not a curvature in time. If time dilation is the same everywhere in a region, then there is no curvature of time in this region. The curvature of time is a change in the time dilation along a spatial direction. For example, if time dilation increases in the radial direction toward the Earth, then it is this increase (gradient) that is the curvature of time and the cause of gravity. – safesphere Dec 31 '23 at 16:27
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    See: https://en.wikipedia.org/wiki/Ellis_wormhole - “in space-time the curvature of space has nothing to do with gravity (the 'curvature of time’, one could say)”. Most answers in the duplicate are wrong and missing the physical meaning of equations. Time and space are relative, so naturally the spatial coordinates are in the equations, but their values depend on the chosen coordinates. This doesn’t affect the fact that physically the cause of gravity is the gradient of the time dilation. Things fall, because they move in time while their direction of time is curved toward a heavy object. – safesphere Dec 31 '23 at 16:46
  • @safesphere, how is what I stated incorrect? A curvature in time is represented by clocks ticking at different rates, which is exactly what occurs along the radial coordinate of a massive object, which is what the question I asked is related to - hence why I stating "Newtonian gravity" – 4D Menu Systems Dec 31 '23 at 17:56
  • You weren’t wrong in your meaning, just imprecise in wording. Consider a massive spherical shell hollow inside. Something like the Earth with the core removed. There is a constant time dilation inside this cavity - time there moves slower than at the surface. However, there is no gravity there per the Newton’s Shell Theorem (or the Birkhoff’s theorem in General Relativity). Things just float in weightlessness there. So time dilation itself does not cause gravity. Gravity is caused by the change (gradient or spatial derivative) of the time dilation, e.g. in the radial direction. – safesphere Dec 31 '23 at 21:28

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