Your statement "accelerated motion warps spacetime" doesn't make much sense on its own. How is spacetime warped exactly? Can you describe it in a step-by-step physical manner instead of using it as a magic wand?

The effect of Time Dilation makes far more sense if you imagine a rocket accelerating:

https://books.google.com/books?id=t8O-yylU0j0C&lpg=PA7&ots=zD8YCKNu7M&pg=PA7#v=onepage&q&f=falseGRAVITATIONAL TIME DILATION

“ Many of the important features of general relativity can be obtained via rather simple arguments that use the equivalence principle. The most famous of these is the thought experiment that leads to gravitational time dilation, illustrated in figure 1.1. Consider an accelerating frame. which is conventionally a rocket of height h, with a clock mounted on the roof that regularly disgorges photons towards the floor. If the rocket accelerates upwards at g, the floor acquires a speed v = gh / c in the time taken for a photon to travel from roof to floor. There will thus be a blueshift in the frequency of received photons, given by Δv / v = gh / c^2, and it is easy to see that the rate of reception of photons will increase by the same factor.

Now, since the rocket can be kept accelerating for as long as we like, and since photons cannot be stockpiled anywhere, the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time Δt by comparison with an identical clock kept on the floor. Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect. Noting that ΔΦ = gh is the difference in potential between roof and floor, it is simple to generalize this to Δt / t = ΔΦ / c^2 ”

“ Figure 1.1. Imagine you are in a box in free space far from any source of gravitation. If the box is made to accelerate ‘upwards’ and has a clock that emits a photon every second mounted on its roof, it is easy to see that you will receive photons more rapidly once the box accelerates

**(imagine yourself running into the line of oncoming photons)**. Now, according to the equivalence principle, the situation is exactly equivalent to the second picture in which the box sits at rest on the surface of the Earth. Since there is nowhere for the excess photons to accumulate, the conclusion has to be that clocks above us in a gravitational field run fast. ”

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See the bolded above. If you imagine yourself accelerating into the line of oncoming photons it is apparent that physical acceleration would cause the time from the clock to appear to dilate. This is a physical explanation for why acceleration would cause time dilation, and also for why photons are blueshifted or redshifted when traveling horizontally upwards or downwards (Pound Rebka Experiment).

Can you give us a step-by-step physical explanation for how space-time is warped to do this?