Is the current black hole horizon observable?

[Naty1]

I am wondering which black hole horizons might be observed experimentally.


a comment in another thread...(PAllen)

Interestingly, if a planet approaches an event horizon, the horizon grows well before the planet reaches the horizon. The current event horizon reflects (in part) all matter that will eventually be trapped.

Kip Thorne in BLACK HOLES AND TIME WARPS has a nice spacetime diagram for what he calls the absolute (current) and apparent horizons of a black hole.

The apparent or "current" horizon

...is just a point when created...and expands smoothly...before the star's surface shrinks through the critical circumference...

The apparent horizon appears suddenly (I guess instantaneously) as the surface of a star shrinks past the the critical circumference...and concides with the absolute horizon.

I am wondering if, as the absolute horizon expands, it it observable in any way...say via gravitational waves??

A third type: (apparently 'observable')

Leonard Susskind has a slightly different "stretched horizon" he explains in the BLACK HOLE WAR:

...Astrophysicsts has already coined the name stretched horizon for an imaginary membrane just outside the horizon...but I was proposing a real layer of stuff, located a Planck length above the horizon, not an imaginary surface. What's more I claimed that an experiment...say lowering a thermometer and measuring temperature for example, would confirm the existence of horizon atoms...

 

[PeterDonis]

The apparent horizon appears suddenly (I guess instantaneously) as the surface of a star shrinks past the the critical circumference...

This is more or less true (see below for a clarification), but it's not what the passage you quoted just before it describes. I believe the quote you gave from Black Holes and Time Warps was referring to the *absolute* horizon, which is what starts out as a point and expands smoothly.

and concides with the absolute horizon.

The *absolute* horizon intersects the collapsing star's surface just as that surface reaches the critical circumference. After that point (assuming nothing else falls into the black hole), the absolute horizon remains at the critical circumference forever.

The "apparent horizon" is another name for a "trapped surface", which has a precise mathematical definition first given (IIRC) by Penrose sometime in the 1960's. Basically it means a surface at which "outgoing" light rays no longer move outward, because of how much they are bent by gravity. So the apparent horizon does "appear instantaneously" when the collapsing star's surface crosses the critical circumference, because that's the first point at which gravity is strong enough to bend outgoing light rays enough to prevent them from moving outward. After that point (again assuming nothing else falls into the hole), the apparent horizon and the absolute horizon coincide forever.

The difference between the two is that the absolute horizon takes into account, not just how much light "right now" is bent by gravity, but how much it will be bent in the entire future of the spacetime. Consider the event at r = 0 when the absolute horizon first forms and starts expanding outward. A light ray sent outward from that point will move outward; gravity is not strong enough there to bend it back and prevent it from doing so. However, as it moves outward, gravity gradually gets stronger and bends it more and more, until, just at the point where it hits the collapsing star's surface (which is the same point at which that surface crosses the critical circumference), gravity becomes strong enough to keep that light ray from moving outward any further. So right at that point, an apparent horizon forms; but the light ray has been traveling along with the absolute horizon all along. The definition of the absolute horizon takes into account the entire future movement of that outgoing light ray, while the apparent horizon only takes into account how it is bent "right now", at one instant of time.

I am wondering if, as the absolute horizon expands, it it observable in any way...say via gravitational waves??

No, because the absolute horizon is a null surface formed by outgoing light rays. No signal can move faster than light, so no signal can get out to you any faster than the absolute horizon itself expands. Gravitational waves are signals and move at the speed of light, so this applies to them too.

 

[Naty1]

Peter...thanks...a few details you added were beyond what I understood...

First a correction:
I previously posted:

The apparent or "current" horizon

...is just a point when created...and expands smoothly...before the star's surface shrinks through the critical circumference..

and yes, I should have said "absolute" instead of "apparent"...

//////////////////

Peter: You mention several issues which I have also read but mayn not understand:

After that point (again assuming nothing else falls into the hole), the apparent horizon and the absolute horizon coincide forever.

But when the hole swallows additional mass or energy, they again expand differently, right?

Consider the event at r = 0 when the absolute horizon first forms and starts expanding outward. ... However, as it moves outward, gravity gradually gets stronger and bends it more and more, until, just at the point where it hits the collapsing star's surface

So an infalling observer experiences more and more gravity while an outgoing one does also?? If so, is this one of the apparent frame of reference "paradoxes" in GR?


But originally I was asking: Can we ever hope to obtain observational evidence for any or all of these horizons?

 

[PeterDonis]

yes, I should have said "absolute" instead of "apparent"...

Ok, good.

But when the hole swallows additional mass or energy, they again expand differently, right?

Yes. Let's say we have a hole with critical circumference C1, which then swallows some more mass-energy, so that its final critical circumference is C2. Let's say the incoming mass-energy arrives as a collapsing spherical shell that is very thin, so we can idealize it as reaching the new critical circumference, C2, all at the same time (call this time T). What will happen to the horizons?

The apparent horizon will jump instantaneously from C1 to C2, at the instant of time where the incoming spherical shell of mass-energy reaches C2, time T.

The absolute horizon will expand smoothly from C1 to C2, starting some time before time T, and reaching C2 at T, just as the apparent horizon jumps there. Thereafter (again, assuming no further mass-energy falls into the hole), the two remain together.

The reason the absolute horizon starts expanding *before* time T, once again, is that the absolute horizon takes into account the future paths of light rays, whereas the apparent horizon does not. For example, suppose there is a lamp emitting light outward at some circumference between C1 and C2. Up until time T, outgoing light rays emitted by that lamp will move outward; the apparent horizon is still at C1. But at some time *before* T, a light ray emitted outward from that lamp will reach C2 at precisely T (because the ray has to travel some distance outward to reach C2, which takes some time). And an outgoing light ray reaching C2 at precisely T can't go outward any further, because at that point the apparent horizon is at C2 and outgoing light there is bent enough that it can't go outward any more. So at the event when the lamp emits an outgoing light ray that reaches C2 at precisely T, the absolute horizon must be expanding outward and just passing the lamp. (In fact, the outgoing light ray emitted by the lamp at that time lies on the absolute horizon.)

So an infalling observer experiences more and more gravity while an outgoing one does also?? If so, is this one of the apparent frame of reference "paradoxes" in GR?

No. I may have mis-stated this a little, or at least not described it very well. The reason I said gravity gradually gets stronger is that I was thinking of a more realistic scenario where the collapsing matter of the star is distributed throughout the space inside its surface; that is, when the absolute horizon forms at r = 0, it is not in empty space, but inside the star's substance. That means that as the absolute horizon expands outward, the substance of the star that it is moving through is getting denser, so gravity is getting stronger.

Let's idealize this situation too, to make things simpler. Let's say that the collapsing matter is not a "star" exactly, but a very thin spherical shell, so that all of the matter reaches its critical circumference, C1, at the same time, call it T1. Inside the shell is empty space, meaning that before time T1, at any circumference at or below C1, there is vacuum.

In this case, the absolute horizon forms at r = 0 at some time before T1 and expands outward at the speed of light. Since it's expanding through empty, flat spacetime (vacuum spacetime inside a spherical shell of matter is flat), its expansion looks just like an ordinary light-cone in Minkowski spacetime; it sees *no* gravity. Only when it reaches C1, at the same instant that the collapsing spherical shell of matter does, does it see gravity; at that time, it takes a sharp "turn", so to speak, as the apparent horizon forms at C1 and outgoing light rays there no longer move outward.

But originally I was asking: Can we ever hope to obtain observational evidence for any or all of these horizons?

In principle the effects of an apparent horizon are certainly observable; just shine a light ray outward and see if it actually moves outward. The problem is communicating a positive result ("outgoing light rays aren't moving outward--apparent horizon present!") to the rest of the universe. "From the outside", so to speak, we can obtain indirect evidence that apparent horizons exist, by looking for mass-energy that "disappears" from observation (no light from it gets back to us) into a region where there is clearly strong gravity. That's basically what astronomers are talking about when they talk about observational evidence for black holes.

The absolute horizon isn't really an "observable thing", because, as I've noted, its location depends on the entire future of the spacetime. In the real universe, we don't know the entire future of the spacetime, so we can't know the exact locations of any absolute horizons. We can only approximately calculate their locations by making assumptions about what the future might look like (e.g., that no further mass-energy will fall into a black hole) that are never precisely accurate.

 

[Naty1]

Peter:

The absolute horizon isn't really an "observable thing", because, as I've noted, its location depends on the entire future of the spacetime...

good stuff...thanks...I've been wondering abnout that for quite a while.