Event Horizons = Cosmological Horizons?

[Salamon]

I wanted to know whether there exists any sort of theory which treats event horizons and cosmological horizons as equivalent.

We can never receive any information from inside of a black hole because this would require an object moving faster than the speed of light to escape from the gravitational field of the black hole.

We can never receive any information from beyond the cosmological horizon because the space itself is traveling faster than the speed of light beyond this distance.

Can it be that these horizons are really the same thing?

For example, the expansion of space at a speed faster than the speed of light in our universe's frame is really equivalent to our universe being viewed as a black hole in another universe's frame?

 

[bapowell]

During inflationary expansion, the cosmological horizon is an event horizon. Your reasoning isn't quite right about this though. During expansion, there is a distance from the observer at which recession velocities become greater than light -- this is the Hubble length. While it is true that galaxies beyond the Hubble length are today moving faster than light, the Hubble length itself is growing in time more quickly than the expansion, and so eventually these galaxies will become observable. This is distinctly different from inflationary (exponential) expansion, during which the Hubble length grows more slowly than the expansion: in this case, objects that are outside the cosmological horizon will be forever so, and the Hubble length marks the event horizon of the observable universe.

 

[Naty1]

Let's do the two 'easy' parts first.

For example, the expansion of space at a speed faster than the speed of light in our universe's frame is really equivalent to our universe being viewed as a black hole in another universe's frame?

Other universes probably can't 'view' us. BUT, observers beyond our cosmological horizon IN THIS UNIVERSE, outside on the other side of our cosmological horizon, would view our 'side of the horizon' generally as described by bapowell...They would not be aware of our [locally viewed] horizon...they have their own view. [see below] Some would eventually be able to see part of our universe, some, further distant would see less, and some would never even get a chance to peek into our 'turf'.

I wanted to know whether there exists any sort of theory which treats event horizons and cosmological horizons as equivalent.

yes. The Holographic Principle, maybe string theory, and maybe ADS/CFT of Maldecena [see wikipedia]. But there may also be some mathematical distinctions...I'm not sure about how experts interpret/explain that.

Here is one possible 'distinction':

Wikiepdia says:
"There are two ways to describe a spacetime with a horizon: locally and globally. The local picture includes only what is (potentially) visible from a given point in spacetime, while the global picture includes unobservable regions beyond the horizon. ... The local and global points of view have different notions of time. From the local point of view the horizon is infinitely far in the future and nothing ever arrives at it, whereas from the global point of view the horizon is an ordinary surface at finite time, and both space and time extend beyond it.

[I think an example of the above is the 'global' Schwarzschild horizon solution ...the one we usually read about. Apparently it took quite some time for scientists/mathematicians to figure out if it was a 'physical entity' or not...what a free falling LOCAL observer would detect [or not] when passing. It turned out to be a coordinate not a physical effect locally. ]

Also, in an expanding universe, an observer may find that some regions of the past cannot be observed ("particle horizon"), and some regions of the future cannot be influenced (event horizon). Examples would be the current particle horizon or ‘surface of last scattering’ after the big bang represents the largest comoving distance from which light could have reached an observer by a specific time, while the cosmological event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future.

On the Holographic Principle:

[The following is my own synopsis from Leonard Susskind's book THE BLACK HOLE WAR:

All information about any region of space is stored on the boundary of that space, but where a particular bit of information is located does not have a unique answer. At each selected volume of space, everything enclosed may be described as a holographic image...a two dimensional surface representation. When we go looking for the hologram it is also always out at the next level of enclosure. Eventually the cosmological horizon reflects all information within the universe.

String theory mathematics places every bit of information at the outer edges of the universe or infinity if the universe is unbounded. Quantum jitters cause fluctuations so violent that a particle would spread to the ends of the universe and such quantum mechanical uncertainty operates even on a scale as large as a black hole event horizons.

Additionally, a related realization of the holographic principle is the AdS/CFT correspondence of Juan Maldacena. Everything that takes place in the interior of anti de Sitter space (a type of space with negative curvature) is an image of reality, a hologram, coded on another type space with fewer dimensions.

He showed a particular quantum theory without gravity is a translation of – is indistinguishable from - another quantum theory that includes gravity but is formulated with one more space dimension. So it seems the form of space time, the number of dimensions for example, is an adorning detail that can change from one formulation to another rather than being a fundamental constituent of reality.

Finally, another possible dictinction...It may be worth noting even in flat Minkowski space an accelerated observer in Rindler space has an associated 'horizon'; What's even 'crazier' radiation [temperature] appears...called Unruh radiation. Does radiation theoretically appear from any other horizons...black hole,yes...others?

PS: I see I missed some horizons:
http://en.wikipedia.org/wiki/Horizon_(general_relativity )
PSS: "Null surface" might be another topic you might search...I remember at least one discussion in these forums.

 

[Naty1]

I wanted to know whether there exists any sort of theory which treats event horizons and cosmological horizons as equivalent.

Just occurrred to me: How about the theory of General Relativity?

 

[bapowell]

yes. The Holographic Principle, maybe string theory, and maybe ADS/CFT of Maldecena [see wikipedia]. But there may also be some mathematical distinctions...I'm not sure about how experts interpret/explain that.

We don't need to refer to these ideas to understand cosmological event horizons; they were first explored within the context of good old QFT in curved spacetime by Gibbons and Hawking in 1977: http://journals.aps.org/prd/abstract/10.1103/PhysRevD.15.2738

If the expansion rate is accelerating, there is a cosmological event horizon and an associated "de Sitter" temperature completely analogous to Hawking radiation at the event horizon of a black hole. In fact, the two types of horizon are mathematically quite similar: both are null surfaces distinguished by the fact that the timelike Killing vector becomes spacelike across the horizon (becomes null on the horizon), and this result is manifested physically as a surface gravity associated with the horizon. This surface gravity is proportional to the temperature of the horizon.

 

[Naty1]

In fact, the two types of horizon are mathematically quite similar: both are null surfaces distinguished by the fact that the timelike Killing vector becomes spacelike across the horizon (becomes null on the horizon), and this result is manifested physically as a surface gravity associated with the horizon. This surface gravity is proportional to the temperature of the horizon.

I recognize most of that from past discussions.

Do you recall a forum discussion about horizons and null vectors [edit: should be 'surfaces]...seems like maybe somebody I trust said there were both 'one sided' and 'two sided' horizons...in other words, a distinction...but I did not keep any link nor notes I could find...

I'll search more...this a subject I find especially fascinating...

 

[Naty1]

I cannot find a definitve information regarding 'equivalence' as queried by Salamon...and GR seems only a general framework of commonality between BH and cosmological horizons...

The Schwarzschild BH solution 'event horizon' involves a theoretically static global spacetime, yet the appearance of Hawking radiation excludes that exact symmetry...it also involves quantum corrections.
The FLRW cosmological model and associated cosmological horizon also depends on a global spacetime but depends exclicitly on an accelerating uniform spacetime...Rather different environments it seems to me.

Here are excerpts from a paper linked in another discussion in these forums...

Hawking radiation from the cosmological horizon in a FRW universe http://arxiv.org/abs/1007.4044v3

June, 2011

It is well known that there is a Hawking radiation from the cosmological horizon of the de-sitter spacetime and the de-Sitter spacetime can be a special case of a FRW universe. Therefore, there may be a corresponding Hawking radiation in a FRW universe.

Event horizon and cosmological horizon are both global concepts . Strictly speaking, locally it is not known whether there is an event horizon or cosmological horizon associated with a certain dynamical spacetime at some time...the event horizon and apparent horizon for a dynamic spacetime are usually different, while they are consistent for a stationary spacetime. So from which horizon the Hawking radiation appears….is still and open question….

As discussed in these forums elsewhere, particle production results from gravitational inhohogeneities in an expanding space-time so how all this compares seems rather mathematically complex.

 

[bapowell]

The particle production in both cases -- Hawking and cosmological -- have the same mathematical origin, namely, the Bogoliubov transformation from the vacuum into a thermal state. You'll notice that the early papers on cosmological particle production (Parker, Ford, Fulling, and others) don't refer to the created quanta as "inhomogeneities". AFAIK, this terminology wasn't fixed until the theory was applied to inflaton fluctuations with the advent of inflation.

Of course, the important distinction to be made here is that de Sitter and Hawking temperatures are directly due to the global horizons in each case; no such horizon exists in general for non-accelerating FRW spaces, although the Bogoliubov transformation still implies physical particle production. I do not know the answer to that.

 

[BertMorrien]

It struck me that there should be an equivalence between the event horizon of a black hole and the 'horizon' of the observable universe. Googling brought me at this blog, so apparently other people have been thinking along the same line of reasoning.
There should be even the equivalence of Hawking radiation, because when particle pairs are formed at either horizon, one of its members could be observed while the other escapes observation. It makes me wonder if our universe as observed by us is nothing more than our perspective from the inside of an ordinary black hole.

 

[bapowell]

It struck me that there should be an equivalence between the event horizon of a black hole and the 'horizon' of the observable universe. Googling brought me at this blog, so apparently other people have been thinking along the same line of reasoning.
There should be even the equivalence of Hawking radiation, because when particle pairs are formed at either horizon, one of its members could be observed while the other escapes observation.

Yes, the cosmological horizon does have a temperature, called the de Sitter temperature, $T = H/2\pi$, where $H^{-1}$ is the radius of the horizon. Notice that it is a factor of 2 larger than the analogous expression for the Hawking temperature. It is sometimes suggested that this is because both particles of the matter/anitmatter pair are observable outside the cosmological horizon, whereas only one is observable outside the event horizon of a black hole. However, I caution against interpreting de Sitter and Hawking radiation too literally in terms of particle creation in this manner, since neither calculation actually describes this process. I recommend reading through several of the posts in this thread for more background on the similarities and differences between black hole and cosmological horizons and their associated particle production.

It makes me wonder if our universe as observed by us is nothing more than our perspective from the inside of an ordinary black hole.

Why?

 

[BertMorrien]

Why? The reason is imho very simple.
Since we cannot say anything definitive about what is beyond either horizon, we can speculate freely about it.
Because our universe has no boundary, the 'shape' of the observable universe (OU) is topologically equivalent to the 'shape' of the unobservable universe (UU).
We know that anything, even a ray of light, cannot cross the event horizon, it remains on the surface.
The same is apparently true for any ray of light in the UU that travels in our direction, because we can never observe it.
Moreover, we cannot observe any ray of light in our OU that travels away from us to either horizon.
Coincidence? Inconsistent with current cosmological models? Maybe, I don't know.
If there are no experiments conceivable that prove that I am wrong, maybe more simple cosmological models are possible.

 

[Chronos]

Assuming I understood the question, I would think the answer is no, the surface of last scattering is not equivalent to the event horizon of an ordinary black hole. The CMB background temperature is 2.72K which is equivalent to that of a subsolar mass Schwarzschild black hole.The universe is rather obviously more massive than the sun.

 

[BertMorrien]

[The CMB background temperature is 2.72K which is equivalent to that of a subsolar mass Schwarzschild black hole.]
I understand that, but only if you assume that the UU itself is a black hole (BH); this is not what I assumed, I assumed that our OU is a BH for a hypothetical observer in the UU. However, your remark is relevant, because the 2.72K thermal radiation could suggest that for us the UU represents a very small BH.
Exactly how obvious is it that the universe is much bigger than the observable universe? Could it be that the data is consistent with a universe that is in essence not bigger than the observable universe?
When the UU is indeed a subsolar mass BH, the prediction is that it would loose mass due to the radiation and the BH temperature would go up and eventually the UU would cease to exist with a bang. So in principle my idea could be experimentally verified by a demonstration that the 2.72K temperature is increasing.
I suspect that the effect is too small to be observed and that the UU will be with us for quite a while.
Maybe somebody can put some numbers here.
But don't take this too seriously, I only brought it up as a thought experiment.
Anyway, thanks for the responses.

 

[bapowell]

Why? The reason is imho very simple.
Since we cannot say anything definitive about what is beyond either horizon, we can speculate freely about it.

Not too freely. We shouldn't speculate that beyond either horizon is only marshmallows.

Because our universe has no boundary, the 'shape' of the observable universe (OU) is topologically equivalent to the 'shape' of the unobservable universe (UU).

I don't understand this. The shape of the ou can be observed. It has trivial topology. We do not know if this is the case for the uu.

We know that anything, even a ray of light, cannot cross the event horizon, it remains on the surface.

Fly a rocket ship directly at a black hole. I assure you that you, including any photons you may have on your person, will fall into it. It won't be pretty.

The same is apparently true for any ray of light in the UU that travels in our direction, because we can never observe it.

Only if the ou isn't growing, but it is.

 

[bapowell]

Coincidence? Inconsistent with current cosmological models? Maybe, I don't know.
If there are no experiments conceivable that prove that I am wrong, maybe more simple cosmological models are possible.

cf. https://en.m.wikipedia.org/wiki/Philosophic_burden_of_proof

 

[BertMorrien]

bapowell,

Me thinks that if we can observe the CMB, we do not observe the unobservable universe here.
But feel free to try again.

 

[bapowell]

bapowell,

Me thinks that if we can observe the CMB, we do not observe the unobservable universe here.

Where do you think the CMB that we will observe in the distant future will be coming from? Your assertion that we cannot observe light emitted towards us from outside the observable universe is false: everyday more and more stuff becomes observable because the Hubble radius is growing.

But feel free to try again.

Not the most humble attitude if you're intent on learning something.

 

[BertMorrien]

bapowell,

Thanks for your response.
I am not trying to be humble, that is not productive.
I wrote: "Since we cannot say anything definitive about what is beyond either horizon, we can speculate freely about it." Your response: "Not too freely. We shouldn't speculate that beyond either horizon is only marshmallows."
In general we should make no assumptions about things we cannot observe in any conceivable way. Normally I try to ignore things we cannot observe.
I still think that the UU is indistinguishable from a BH. Another thing is that if something falls to a BH, it is accelerated. The same acceleration is observed most clearly for galaxies near the horizon of the observable universe.
About the growing of the observable universe, you apparently assume that the new things becoming observable pre-existed in the UU. Maybe you see the similarity between this and the pivoting role of observation in quantum mechanics. If a particle is observed, you are not allowed to say something definitive about that particle before the observation.
I think I did not make any assumption about what event horizons hide, the only thing I did was pointing to things that can be observed. I think it's the theoretical physicists who make suppositions about unobservables. Lawrence Krauss gets a universe from 'nothing'. If one thing is fundamentally unobservable, then it is 'nothing'. I believe that what cannot be observed should stay out of any discussion. I think that you cannot avoid to notice that the 'nothing' of Krauss is untenable, at least you must assume that uncertainty always exists. It is very difficult to be completely unbiased. I am not so sure the 'traditional' cosmological model is free from bias.

 

[bapowell]

bapowell,

Thanks for your response.
I am not trying to be humble, that is not productive.
I wrote: "Since we cannot say anything definitive about what is beyond either horizon, we can speculate freely about it." Your response: "Not too freely. We shouldn't speculate that beyond either horizon is only marshmallows."
In general we should make no assumptions about things we cannot observe in any conceivable way. Normally I try to ignore things we cannot observe.
I still think that the UU is indistinguishable from a BH.

One way that it's not, that I've just mentioned twice, is that photons can move from the unobservable universe into the observable universe. As you've stated already, the same is not true for a photon inside a black hole.

Another thing is that if something falls to a BH, it is accelerated. The same acceleration is observed most clearly for galaxies near the horizon of the observable universe.

No, galaxies near the cosmological horizon are not accelerated in this manner. For a black hole, $a \propto 1/r^2$, whereas the acceleration experienced by a comoving object in the universe is constant.

About the growing of the observable universe, you apparently assume that the new things becoming observable pre-existed in the UU. Maybe you see the similarity between this and the pivoting role of observation in quantum mechanics. If a particle is observed, you are not allowed to say something definitive about that particle before the observation.

Yes, I assume that a CMB photon that is observed a million years from now on Earth originated outside of today's observable universe. How else is this possibly to be interpreted? I don't see what quantum mechanics has anything to do with it.

 

[BertMorrien]

bapowell,Like I said before, don't take this too seriously. I think there really was a Big Bang, and I think the CMB is really a remnant of it.
I suspect that I am not the only one who is confused by trying to get a mental image of the universe. You have to take into account that the further away you look in space, the further you look back in time and the slower the observed 'clocks' are running. I am sure these are not the only factors that you must take into account. Our brain has simply not evolved to cope with these kinds of problems. Some of us, not me, can approach the universe mathematically and maybe some can even develop an intuitive understanding of it. Not me, and that is frustrating. The universe is complex.
Again, thanks for your responses.