Equilibrium of Universe: Earth vs. Black Hole

[durant35]

I have a question regarding the process of getting towards equilibrium in our universe. If we imagine a causal patch with our planet at the centre, every planet will redshift away from us an after a while the planet itself will disintegrate, let's call this process the decay of Earth. Eventually after all particles move out this causal patch what is left will be empty space - the maximum entropy state.

However let's imagine a causal patch/observable universe which has a black hole in its center, Black holes take longer to 'decay' than planets or stars due to slow evaporation. After the particles move away from this causal patch there will be nothing left but empty space. If we compare this process of 'emptying out' in the black hole's causal patch with Earth's causal patch presumably Earth will 'decay' much faster than the black hole, so the equilibration in causal patch of the Earth will be much faster than equilibration in causal patch of the black hole.

To sum up, is it legit to say that different parts of the universe equilibrate (or asymptote towards empty space) at different rates depending on the matter content inside them? If we look globally, the process of emptying out isn't something that happens at the same rate?

This thought has come up to my mind while reading the wikipedia article: https://en.wikipedia.org/wiki/Future_of_an_expanding_universe
where it is clearly stated that the 'Black hole era' will happen much later than the dinsintegration of planets.

If this is valid, is it correct to conclude that our observable universe will empty out much faster than let's say an observable universe of a black hole ?

Thanks in advance

 

[kimbyd]

Minor point:
The Earth won't be left alone due to the expansion. Gravitationally-bound systems won't be carried away by the expansion, so that many galaxies close to our own will always remain within our horizon. So you won't get single causal patches with only a black hole or a planet at their centers. You'll have a large collection of matter within each patch. I don't know precisely how that matter will evolve, but I think that eventually all of the matter within the patch will eventually decay, leaving only a group of black holes. The question then becomes whether the orbits of those black holes decays faster or slower than the decays of the black holes themselves. But either way the end state of every causal patch becomes one with one or more black holes in it, black holes which eventually decay.

The rate of equilibration can vary dramatically, however, based upon the precise masses of the black holes within the patch. Some patches will not have very massive black holes, and thus will decay relatively rapidly compared to patches with much more massive black holes.

For comparison, a solar-mass black hole will decay after about $10^{67}$ years, while a billion solar mass black hole will take about $10^{94}$ years to decay. So if you had a causal patch that had nothing but very small dwarf galaxies that only ended up with a handful of solar-mass black holes, then that patch will become empty space far more rapidly than a patch with a massive galaxy with a billion-solar-mass black hole at its center.

And if black hole orbits tend to decay more rapidly than they tend to evaporate, their masses will grow and they'll take much longer to dissipate.

 

[guywithdoubts]

after a while the planet itself will disintegrate, let's call this process the decay of Earth.

I don't know precisely how that matter will evolve, but I think that eventually all of the matter within the patch will eventually decay

Quick question, are you assuming protons to decay or am I missing something else?

 

[PeterDonis]

John Baez has an article that is relevant to this topic:

http://math.ucr.edu/home/baez/end.html

 

[durant35]

Minor point:
The Earth won't be left alone due to the expansion. Gravitationally-bound systems won't be carried away by the expansion, so that many galaxies close to our own will always remain within our horizon. So you won't get single causal patches with only a black hole or a planet at their centers. You'll have a large collection of matter within each patch. I don't know precisely how that matter will evolve, but I think that eventually all of the matter within the patch will eventually decay, leaving only a group of black holes. The question then becomes whether the orbits of those black holes decays faster or slower than the decays of the black holes themselves. But either way the end state of every causal patch becomes one with one or more black holes in it, black holes which eventually decay.

The rate of equilibration can vary dramatically, however, based upon the precise masses of the black holes within the patch. Some patches will not have very massive black holes, and thus will decay relatively rapidly compared to patches with much more massive black holes.

For comparison, a solar-mass black hole will decay after about $10^{67}$ years, while a billion solar mass black hole will take about $10^{94}$ years to decay. So if you had a causal patch that had nothing but very small dwarf galaxies that only ended up with a handful of solar-mass black holes, then that patch will become empty space far more rapidly than a patch with a massive galaxy with a billion-solar-mass black hole at its center.

And if black hole orbits tend to decay more rapidly than they tend to evaporate, their masses will grow and they'll take much longer to dissipate.

Hey, thanks for the detailed answer.

So is it legitimate to say that that different causal patches equilibrate/asymptote to de Sitter depending on their matter content? I'm keen to connect this to some holographic ideas which are quite popular in recent times. It seems to me that the duration of the matter/radiation dominated period of our universe depends on the matter content/energy and that some parts equilibrate faster and some slower, just like a bigger black hole evaporates slower than a smaller black hole

 

[kimbyd]

Hey, thanks for the detailed answer.

So is it legitimate to say that that different causal patches equilibrate/asymptote to de Sitter depending on their matter content? I'm keen to connect this to some holographic ideas which are quite popular in recent times. It seems to me that the duration of the matter/radiation dominated period of our universe depends on the matter content/energy and that some parts equilibrate faster and some slower, just like a bigger black hole evaporates slower than a smaller black hole

The matter/radiation dominated period of our universe is already over. Our universe is now dominated by dark energy. The expansion rate of our universe will behave in a manner indistinguishable from de Sitter space long before all matter is gone.

But it is fair to say that the rate at which each causal patch evolves to an eventual empty-space state can vary dramatically depending upon the configuration of matter within that patch.

 

[kimbyd]

Quick question, are you assuming protons to decay or am I missing something else?

Proton decay is typically assumed in these calculations, yes. Some magnitude of proton decay is unavoidable, as discussed here:
https://en.wikipedia.org/wiki/Futur...otons_decay_on_higher_order_nuclear_processes

One way to understand why it's impossible for there not to be proton decay is that protons in our universe were created through some process. However convoluted that process was, its time reverse must be possible. Most theories of proton decay suggest that it will result in black holes lasting far longer than normal matter. But there are some theories that extend proton lifetimes long enough that there will be normal matter out there after all black holes decay.

 

[rootone]

What happens when the final proton that once was a member of what we call the Universe decays?
Nothing much is my best guess.