Let's say Alice and Bob are stationary to each other in the same place, then Bob begins to constantly accelerate away from Alice. When Alice's clock reads that some time has passed on her clock, she would say that the same amount of time has passed for Bob, but time dilated. In terms of just SR, that would be t' = Int dt sqrt[1 - (v/c)^2], time dilated only according to the instantaneous relative speed, where v/c = (a t / c) / sqrt[1 + (a t / c)^2], so t' = Int dt sqrt[1 - (a t / c)^2 / (1 + (a t / c)^2)] = Int dt sqrt[((1 + (a t / c)^2) - (a t / c)^2) / (1 + (a t / c)^2)] = Int dt / sqrt[1 + (a t / c)^2] = (c / a) * asinh-1(a t / c) = (c / a) * ln[(a t / c) + sqrt(1 + (a t / c)^2)]Does all of that look correct? Here is the problem. It accounts for time dilation in SR, but does not seem to account for gravitational time dilation with the fictional gravity that acts upon the accelerating observer in order to accelerate. So shouldn't there be another term in the integration for that as well?