I've made an error in my thinking somewhere concerning gravitational waves in the following thought experiment, and would appreciate knowing where I went wrong:
Consider two overlapping gravitational waves, with regions both ahead and behind the overlapping area. Relative to a far away observer, the overlapping area would be traveling slightly below c, due to gravitational time dilation.
As a result, the region behind the overlapping area of the two gravitational waves would eventually 'catch up' to the overlapping area. However, once any portion of that region enters the overlapping area of the two waves, relative to the far away observer, it would appear to travel at the same speed as the overlapping region, slightly slower than c.
Considering that, according to current theory, it is impossible to observe events below the Planck length and time (and further, that such notions become meaningless, in that quantum gravitational effects become important, and classical notions of space and time break down) the observer would, according to this assumption, only be able to observe the effects of the overlapping area on the incoming region of the gravitational wave (and vice versa) after a Planck time (at absolute minimum) or when the incoming region of the wave had traveled a Planck length into the overlapping area.
Therefore, when such conditions are satisfied, the far away observer sees that the incoming portion of the wave has traveled a Planck length into the overlapping region, and is now traveling at the same speed as the overlapping area of the two waves. This process repeats until the entire region of the waves situated initially behind the overlapping area of the two gravitational waves has been 'compressed' into a Planck length.
Eventually said region 'splits off' from the initial overlapping area, once the gravitational time dilation of the 'compressed' region becomes significant enough to observe, as all portions of the incoming wave that was initially situated behind the overlapping region affect each other, producing a collective slow down relative to the observer.
