Summary:

I know of two interpretations to the mechanics of how time dilation works. Have we advanced enough in probing the interior of the sun to be able to find evidence to distinguish between these two models?

Details:

In the first and most accepted model, time dilation is caused by the differential of gravitational fields between two points. In the second model, mass causes the curvature of space time which results in gravity. The curvature of space time itself is time dilation.

Examples of putting these two concepts into practice. In the first model, you would reach maximum time dilation in the sun at a depth of 1/2 radius, and approach zero time dilation from the solar gravity at the center being in equilibrium. Conversely in the second model, maximum time dilation would occur in the center.

I understand that the formulas are a two body system which is why the first model is the primary accepted theory. My question is, have we reached the technological level to find physical data to support this argument?