I guess the conclusion I'm hoping to draw is that the two types of time dilation, one due to a velocity approaching speed of light and the other due to the warping of spacetime near great mass densities are actually the same and that the second, described by general relativity, is in fact...
If you solve for the velocity though you get the expression for escape velocity.
$$v_e=\sqrt{\frac{2GM}{r}}$$
Forgive me for being stubborn, I'm just trying to connect dots
Looking at the two equations for time dilation they seem very similar
$$t_{surface} = t_{space} \sqrt{1-\frac{2GM}{rc^2}}$$
$$t_{moving} = t_{observer}\sqrt{1-\frac{v^2}{c^2}}$$
I was hoping someone could explain more how they are connected?
I'd like to think that a fast moving object...