# Entropy limit inside event horizons

1. Oct 11, 2013

### friend

As I understand it, the entropy inside a horizon, the black hole event horizon or the cosmological event horizon, is limited by the entropy proportional to the surface area of that horizon. My question is: does that entropy limit always allow the possibility for maximum entropy of the material inside - to a completely thermalized gas? Or would that horizon entropy limit prevent the complete dissipation of structure inside, in some cases?

2. Oct 11, 2013

### friend

For example, stuff falls into a black hole. Then the black hole evaporates and becomes smaller. The smaller surface area means the entropy inside now has a lower upper limit to the entropy for the same amount of stuff that originally fell inside. How does the matter that fell in arrange itself to accommodate an ever decreasing limit to the entropy as the BH evaporates?

3. Oct 18, 2013

### friend

And then there is the cosmological event horizon, the distance at which galaxies are receding faster than the speed of light. We can no longer see galaxies that are further away, and there is an event horizon at that distance that surround us. And associated with that horizon surface is an entropy proportional with the area of that surface.

But we've recently discovered that the expansion of the universe has accelerated. I understand this to mean that the recession speed of receding galaxies has increase, and so the distance at which galaxies are receding faster than the speed of light is getting smaller. So the horizon surface is shrinking and with it the entropy proportional to that surface area must also be decreasing.

The question is how has matter inside the cosmological event horizon accommodated a shrinking horizon and the decrease of entropy of that horizon? Does gravity cause things to clump together to offset this reduction in entropy of a shrinking horizon due to acceleration in expansion? Does life form on a few planets inside the volume of this shrinking horizon? Or do galaxies recede behind the horizon whose entropy is equal to the amount of entropy decrease of the shrinking horizon? Or for that matter, does in fact the cosmological event horizon shrink with accelerated expansion rates.