Is the event horizon of a black hole physical?

[PAllen]

The 'location' of a black hole's event horizon is a frame dependent measurement [i.e., relative]. What a remote observer perceives is not the same as that of an infalling observer, and reconciling the two perceptions is no trivial matter. On this basis it could be argued the event horizon is purely subjective, lacking any objective sense of 'physicality'. For discussion, see http://www-e.uni-magdeburg.de/mertens/teaching/seminar/themen/touching_ghosts.pdf

Actually I think this article is in error in a few points. One thing they don't show in fig. 4, but is obvious from the defining characteristics of Kruskal coordinates, is that a signal sent by A just after A crosses the horizon reaches B before B reaches the singularity. Also, if B was infalling sufficiently close to A, that B could send a signal inside the horizon that reaches A before A reaches the singularity. (In their figure, they have the B infaller too far behind A for this to happen).

There is a statement in fig. 4: "This is an
asymptotic process as no signal can be emitted at the horizon (there can be no ‘trapped’ signal)." that I think is just wrong. A signal can be emitted emitted at the horizon and be trapped.

The ghostly appearance they claim is a misleading description of what is seen. In fact, no strange image is seen. That B sees A crossing the horizon only when B crosses the horizon is well known and is not mysterious in appearance. Simply consider things from B's free fall frame. B continuously gets signals from A. Now imagine a series of infallers ahead of B (A1, A2, A3). For B, these move on a radial line in 'front' of B. Now imagine a radio signal emitted from somewhere at smaller r than A, forming a spherical wave. This outgoing wave has all the properties of the event horizon (it is an outgoing null surface). When B gets this radio signal, they see A1 as of when this signal passed A1; they see A2 as of when this signal passed A2; etc. You could set this up on a long train, and not consider anything mysterious to happening. The 'mystery' occurs only by forgetting that the horizon is just an outgoing null surface from the point of view of infallers. If you actually set this up, assuming B could not see radio waves, they would not disinguish their crossing the horizon from any other moment; the way prior infallers look would be indistinguishable from just before to just after B crossed the horizon.

 

[Chalnoth]

The 'mystery' occurs only by forgetting that the horizon is just an outgoing null surface from the point of view of infallers. If you actually set this up, assuming B could not see radio waves, they would not disinguish their crossing the horizon from any other moment; the way prior infallers look would be indistinguishable from just before to just after B crossed the horizon.

...unless there is a firewall at the horizon that fries all of the infalling observers upon horizon crossing...

 

[Naty1]

Here is what I believe is a confirmation of my abbreviated explanation in post #60:

… [The event horizon of a BH is not a physical object, it is a mathematically defined boundary (corresponding to physical phenomena).]..


We can recover the analogy however if we look more closely at what happens when a physical clock (or other real object) falls into a BH rather than just the behavior of the future geodesic path of the object.

Remember that an infalling physical object will have some mass or at least momentum-energy. So the full description of the space-time geometry along the future geodesic will no longer be static. The "infalling object never reaches the event horizon" derivation reflects an idealized limit as the object has zero effect on space-time. This zero effect and infinite time to infall should cancel to a finite outcome.

What should happen (and I'm working heuristically here as I've not seen or done the hard calculations) is that as the infalling object nears the event horizon, the horizon itself should move outward, reflecting the additional curvature of space-time due to the object's mass. Then in a finite time (of the external observer's clock) the event horizon will envelope the object, you'll have a no-longer-spherical BH and its EH will "ring" emitting gravity waves as it settles down to a new ever so slightly larger spherical configuration

 

[Mordred]

I've been looking over how Unruh effect occurs on the cosmological horizon. Finally realized that it may b e better to look at how cosmological horizon is defined.

http://arxiv.org/abs/astro-ph/0310808

the above mentions some of the misconceptions its related so I thought I'd add it.

this link touches briefly on cosmological Hawking radiation

http://www.relativitybook.com/resources/cosmological_horizons.html


Now the paper posted in previous post mentions the De sitter spacetime. which also mentions the De Sitter spacetime is a special case of FRW universe.

So here is my question as I'm only loosely familiar with those terms.

How does the De Sitter model define cosmological horizon ?

 

[Mordred]

Never mind on that last question I located a description which helps me understand the underlying comparision of cosmological horizon as opposed to the event horizon. Now that bloody paper is making more sense lol


De Sitter space is the simplest solution of Einstein's equation with a positive cosmological constant. It is spherically symmetric and it has a cosmological horizon surrounding any observer, and describes an inflating universe. The Schwarzschild solution is the simplest spherically symmetric solution of the Einstein equations with zero cosmological constant, and it describes a black hole event horizon in otherwise empty space. de Sitter–Schwarzschild is a combination of the two, and describes a black hole horizon spherically centered in an otherwise de Sitter universe. An observer which hasn't fallen into the black hole, and which can still see the black hole despite the inflation, is sandwiched between the two horizons.

One natural question to ask is whether the two horizons are different kinds of objects or whether they are they fundamentally the same. Classically the two types of horizon look different. A black hole horizon is a future horizon, things can go in, but don't come out. The cosmological horizon in a big bang type cosmology is a past horizon, things come out, but nothing goes in.

But in a semiclassical treatment, the de Sitter cosmological horizon can be thought of as absorbing or emitting depending on the point of view. Similarly, for a black hole that has been around for a long time, the horizon can be thought of as emitting or absorbing depending on whether you take the point of view of infalling matter or outgoing Hawking radiation. Hawking argued based on thermodynamics that the past horizon of a white hole is in fact physically the same as the future horizon of a black hole, so that past and future horizons are physically identical. This was elaborated by Susskind into black hole complementarity, which states that any interior parts of a black hole solution, in either the past and future horizon interpretation, can be holographically related by a unitary change of basis to the quantum mechanical description of the horizon itself.

 

[Naty1]

How does the De Sitter model define cosmological horizon ?

It's flat space-time, no matter, with a cosmological constant [expansion]...one solution of the FLRW cosmological model...also like the early inflationary era and the final stage of our own universe in the infinite future...

Is this enough:

The exponential expansion of the scale factor means that the physical distance between any two non-accelerating observers will eventually be growing faster than the speed of light. At this point those two observers will no longer be able to make contact. Therefore any observer in a de Sitter universe would see event horizons beyond which that observer can never see nor learn any information. If our universe is approaching a de Sitter universe then eventually we will not be able to observe any galaxies other than our own Milky Way (and any others in the gravitationally bound Local Group, assuming they were to somehow survive to that time without merging).

http://en.wikipedia.org/wiki/De_Sitter_universe#Relative_expansion


This is also the infinite future of black hole horizons... asymptotically flat...

A brief discussion relating deSitter space to black hole horizons and early universe inflationary expansion:

http://en.wikipedia.org/wiki/Cosmological_inflation#Space_expands

If there is something unique about a deSitter horizon, I hope someone can explain it.

 

[Mordred]

well one thing different is the inflation field

The inflaton is the generic name of the hypothetical and hitherto unidentified scalar field (and its associated particle) that may be responsible for the hypothetical inflation in the very early universe. According to inflation theory, the inflaton field provided the mechanism to drive a period of rapid expansion from 10−35 to 10−34 seconds after the initial expansion that formed the universe.

The inflaton field's lowest energy state may or may not be a zero energy state. This depends on the chosen potential energy density of the field. Prior to the expansion period, the inflaton field was at a higher energy state. Random quantum fluctuations triggered a phase transition whereby the inflaton field released its potential energy as matter and radiation as it settled to its lowest energy state. This action generated a repulsive force that drove the portion of the universe that is observable to us today to expand from approximately 10−50 metres in radius at 10−35 seconds to almost 1 metre in radius at 10−34 seconds.

but I think this is what your after on the uniqueness

Unique to universes described by the FLRW metric, a de Sitter universe has a Hubble Law which is not only consistent through all space, but also through all time (since the deceleration parameter is equal to ), thus satisfying the perfect cosmological principle that assumes isotropy and homogeneity throughout space and time. As a class of models with different values of the Hubble constant, the static universe that Einstein developed, and for which he invented the cosmological constant, can be considered a special case of the de Sitter universe where the expansion is finely tuned to just cancel out the collapse associated with the positive curvature associated with a non-zero matter density. There are ways to cast de Sitter space with static coordinates (see de Sitter space), so unlike other FLRW models, de Sitter space can be thought of as a static solution to Einstein's equations even though the geodesics followed by observers necessarily diverge in the normal way expected from the expansion of physical spatial dimensions. As a model for the universe, de Sitter's solution was not considered viable for the observed universe until models for inflation and dark energy were developed. Before then, it was assumed that the Big Bang implied only an acceptance of the weaker cosmological principle which holds isotropy true only for spatial extents but not temporal extents.[2]

 

[Naty1]

Nothing I can see that is unique about your description regarding the horizon [prior post]... that's the wiki description. I already posted this, from PeterDonis:

..The event horizon of a black hole is actually lightlike. This follows from it being a null surface, and you can even think of the event horizon as being "trapped light". “the EH is a null surface--more precisely, it has two spacelike and one null dimension.”
PAllen & PeterDonis…… the event horizon is a 3-surface whose tangent space at each point can be given a basis that has two spacelike basis vectors and one null basis vector…the EH is not a "thing". It's just a boundary between two regions of the spacetime.,,,,

I believe that is a generic description...a null surface is a null surface...applicable to black holes [Hawking radiation] , cosmological horizons ['particle production'], and accelerating observers [Unruh radiation].
From what I can tell so far, they are all similar, very close, but I do not know if 'identical', meaning mathematically equivalent.

I'm pretty sure I asked this same question in another thread and I don't recall ever seeing a answer.

 

[Mordred]

Well that paper appears to treat them as mathematically equivelent whether they are or not is something I would definitely like to know asa well. If you happen to find the answer in the other post or other sources I would be interested.

I'm starting to make headway now on that paper, its slow going as I'm also looking at Hawking radiation and a paper on quantum fluctuations of a vacuum. There is several correlations but its too early for me to describe them.

 

[Naty1]

Here is a description [no source] which I liked:

Let me describe a Rindler horizon scenario. Two ships are accelerating together at 1 g for a long time approaching near c. One of them runs out of fuel and stops accelerating. The accelerating ship will see the out of fuel ship fall a little behind, but then become red shifted, clocks on it appear to slow down and asymptotically stop; red shift grows to infinity. The empty ship becomes invisible. The empty ship is never seen to be farther than a short distance away from accelerating ship, as long as it can be seen at all. It is 'trapped' on the Rindler horizon. Of course, for the empty ship, nothing strange has happened. The other ship accelerates away from it, getting ever further away. The empty ship can receive signals from the accelerating one, but any signals it sends can never reach the accelerating ship (because the accelerating ship stays ahead of the light; no contradiction because it had a head start and keeps accelerating.

This has direct implications for other horizons:
http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

An 'odd' consequence [to me] is that the accelerating ship sees vacuum particles the inertial [out of fuel] ship does not, via the Unruh effect Yet the accelerating ship can't get signals from the inertial ship. The inertial ship receives signals from the accelerating ship but not the extra vacuum signals. This seems a weird information flow!

 

[Mordred]

lol yeah I'm definitely going to have to add that one to my reading material.
and your right it does seem strange on the information side.