In the context of general relativity, the theory of gravity developed by Albert Einstein, gravity is described as the curvature of spacetime caused by the presence of mass and energy. The curvature of spacetime affects the flow of time, resulting in time dilation.
The principle of equivalence in general relativity states that the effects of gravity are indistinguishable from the effects of acceleration. This means that when you are in a gravitational field, such as near a massive object, you can experience effects similar to those experienced in an accelerating reference frame.
In a region of spacetime with a gravitational field, time dilation occurs because the curvature of spacetime causes the flow of time to vary. The strength of the gravitational field, or the curvature of spacetime, is related to the distribution of mass and energy in the vicinity.
The relationship between gravity and the gradient of time dilation comes from the mathematics of general relativity. The gradient of time dilation represents the rate at which the flow of time changes in different regions of spacetime. In the presence of a gravitational field, the curvature of spacetime causes this gradient to vary, and this variation is related to the strength of the gravitational field.
In essence, the connection between gravity and the gradient of time dilation arises from the fundamental principles and mathematical framework of general relativity. It provides a description of how the curvature of spacetime, which is related to the distribution of mass and energy, influences the flow of time and results in the effects we observe as gravity.