Getting back to GoC and puppypower. If gravity lowers entropy (locally only) and increasing gravitational field strength slows down time then there looks like there is an indirect relationship between time dilation and entropy. If an increase in time dilation can be tied to lower entropy then at the event horizon of a black hole the entropy would have to decrease. Yet tidal forces would have exactly the opposite effect. Both can't be true. To resolve this issue there would need to be a velocity dependence on the state of entropy when moving through an increasing gravitational field.

Gravity not only impacts space-time, but gravity also generates pressure. This pressure is separate from space-time as inferred by time. For example, at the bottom of the space-time well time runs slowest. Yet in the center of gravity, which is the same spot, this place of highest pressure, defines phases of matter with the fastest frequencies; matter gets faster. There are two separate layers of time affects.

The simplest way to explain this is, gravity is an acceleration; d/t/t. Using simple dimensional analysis, acceleration is one part distance and two parts time. Space-time is one part distance and one part time. We need to account for the extra time. Pressure makes use of the second unit of time, which in the case of the core of the star, allows the fastest material phase frequencies. This aspect of time (faster) goes the other way compared to the time in space-time (slower).

In special relativity, since we deal with velocity; d/t, which is one part time and one part distance, we don't have to deal with the extra time of gravity. A relativistic space-ship will not implode, due to the extreme pressure that one will see if this reference was based on gravity.

As you go from space to the event horizon, space-time contracts. However, we also have that extra time due to acceleration. The pressure causes matter to assume phases of higher and higher frequency. The entropy change will depend on what these phases are.

For example, if we add pressure to water vapor we can get liquid water. This change of phase from vapor to liquid, by gravitational pressure, causes a drop in entropy. As we increase pressure even more, liquid water molecules will get closer, disrupting low entropy water structures that form in water. These structures depend on the hydrogen bonds being somewhat stretched. If we push these bonds closer, this disrupts the order and causes the entropy of the liquid water to increase.

Theoretically, pressure can make entropy go both ways based on the nature of the new phases and what happens in the phases. Fusion by binding two mobile atoms into one heavier and slower atom, lowers entropy. If we keep adding pressure, we can make the sub particles inside the nuclei to get too close, which may result in larger sub-particle composites with even higher entropy. This may occur when we exceed neutron density.

In the case of event horizon, it all depends on the phases due to pressure and materials. One possible scenario is say the pressure causes phases with extreme frequency and increasing entropy. What does this spectrum look like? If we red shift this extreme spectrum so it is larger, it still may be small to see or detect? The percent difference in the space-time well of the sun is much tighter than the material frequency difference from the surface to the core. We may need an extreme pressure sub-particle film to see it. What is smaller than gamma?