Can a black hole event horizon grow at the speed of light?

[votingmachine]

This is correct. It is correct because the "locational displacement" of the event horizon is not a change in spacetime curvature that has to propagate at the speed of light. It is just a number we can calculate (and the number can be different depending on the coordinates we choose) that has no physical effects. The actual changes in spacetime curvature associated with a black hole growing in mass do propagate at the speed of light, as above.

I've got it now. It was the difference between that propagation of spacetime curvature at the speed of light, from the "movement" of the calculated event horizon that was confusing me.

I find myself saying two contradictory things. The mathematical boundary from a changing mass could move faster than c. And the changing mass can only have effects that move outward from the center of mass at c.

Your answer clears up that the confusion is because I was equating two different things.

 

[George K]

This is misstated. The event horizon is not a "physical surface" of anything. An idealized black hole is a vacuum solution of the Einstein Field Equation; there is no stress-energy anywhere. A more realistic solution describing a hole formed from the collapse of a massive object like a star has a region of nonzero stress-energy occupied by the collapsing object, but that region occupies very little of the interior region (i.e., the region of spacetime inside the event horizon), and anyone falling into the hole well after the collapse will encounter only vacuum at and well inside the horizon.

Also, the mass of the hole is not "inside the event horizon". It is really a global property of the spacetime, not a localized property of anything.

I know that if someone falls into a BH and reaches the EH doesn't "hit" on something. He just passes through it. (In the case of a very large BH he may doesn't even notice that he has passed the EH as the tidal forces are not significant yet.) And he experiences vacuum at and well inside the EH. In fact all the mass of the BH is located at its center, i.e. on its singularity. However, the EH is the "physical limit or boundary" of the BH (although it is not a "physical surface" consisting of something). This means that whatever passes the EH is -from now on- a part of the BH (i.e. it "belongs" to the BH). The calculated mass of the BH is whatever is inside its EH. Whatever passes the EH is added to the BH's mass and as a result the EH is increased accordingly.
The problem is if the EH can be expanded in a speed higher than c (or even if there is any limit at all on this speed). See my post #34. If an object enters the EH on the one side of the BH, the local, asymmetrical expansion of the EH must "travel" all around to the other side of the BH in order this expansion to become global and symmetrical again (i.e. in order to get again a new, spherical EH). And this re-arrangement doesn't happen in zero time. I suppose that this re-arrangement is done via the gravitational waves that are produced during the absorption of this object. And the speed of these waves are c.
Let's take as an example the merging of two BHs (as I said in my post#34). At t₁ the two BHs collide with one another. At this moment the new EH is highly distorted and asymmetrical. A re-arrangement (bouncing) takes place, obviously via gravitational waves. At t₂ the bouncing is settled down and a new, larger and symmetrical (i.e. spherical) EH has been formed. Then we can measure the speed of the EH's increment. And for this measurement we take into account the increment of the EH's size (before and after the collision) that took place in Δt=t₂-t₁. If this is correct, I think that this speed should be c.

 

[votingmachine]

the hypothetical asymmetric growth of a black hole can probably never be measured or observed with any satisfactory accuracy.

Sure it can; LIGO measured it. See above.

Black holes just are not amenable to exact measurement science.

Sure they are. LIGO measured properties of black holes.

LIGO measured slight spacetime distortions that are from a large mass collision, many light years from earth. The masses are too dense to be anything but black holes. I don't want to quibble, but the measurement says the collision happened between 600 million and 1.3 billion light years from earth. I have a slightly different use of the words "exact measurement" and "observed with satisfactory accuracy". LIGO's measurements are fantastic, but I will still hold the opinion that black holes are not likely to be measured with "satisfactory accuracy" ... although I should add, in my lifetime, which is a rather self-centered point of view, but understandable.

LIGO DIRECTLY measured black holes. My understanding is that this is the FIRST time direct measurement of black holes has been accomplished. So progress, as more detectors are added, can be expected. You may have an expectation of much better gravity measurements that allow much clearer views of black holes. That may be reasonable. I hope you are right. I was not really making a careful prediction, but noting that the problem is very difficult.

 

[PeterDonis]

the EH is the "physical limit or boundary" of the BH

Not in the sense you are using that term. See below.

The calculated mass of the BH is whatever is inside its EH.

No, it isn't. As I think I've already said, the "mass" that appears in the metric is a global property of the spacetime; it is not a local property of the region inside the EH. If a large object is falling into the hole, an observer far away will see the same "mass" before it passes the EH as after; the event of the object passing the EH does not change the "mass" observed from far away at all.

So, as I said to votingmachine, the EH can "expand" faster than $c$ because the "expansion" of the EH is not something that causes anything else. All actual causal influences propagate at the speed of light; but the event of an object passing the EH does not produce any causal influence on anything, nor does the EH "expanding".

To go further into this would require going beyond the scope of a "B" level thread; so if you have further questions about how this works, you should start a new thread at a higher level (and you should be prepared to deal with the math that will be required).

 

[PeterDonis]

I was not really making a careful prediction, but noting that the problem is very difficult.

Understood, thanks for clarifying. I agree that the problem is very difficult. I am probably more optimistic than you are about it getting solved somehow. Part of that optimism is simply due to the success LIGO has already had at measuring things that, not too long ago, many people were saying were impossible to ever measure at all. But there is certainly a lot more yet to do.

 

[George K]

Not in the sense you are using that term. See below.
No, it isn't. As I think I've already said, the "mass" that appears in the metric is a global property of the spacetime; it is not a local property of the region inside the EH. If a large object is falling into the hole, an observer far away will see the same "mass" before it passes the EH as after; the event of the object passing the EH does not change the "mass" observed from far away at all.
So, as I said to votingmachine, the EH can "expand" faster than $c$ because the "expansion" of the EH is not something that causes anything else. All actual causal influences propagate at the speed of light; but the event of an object passing the EH does not produce any causal influence on anything, nor does the EH "expanding".
To go further into this would require going beyond the scope of a "B" level thread; so if you have further questions about how this works, you should start a new thread at a higher level (and you should be prepared to deal with the math that will be required).

The question is: What is the exact moment that an outside observer can verify that the mass of a BH has been increased? I know that, essentially, all the mass of a BH is concentrated upon its singularity. So, I suppose that an actual increment of the BH's mass (as observed by an outside observer) occurs when the in-falling object reaches the singularity (i.e. when it is incorporated into the singularity). Is this what you mean?
And if this is correct, this is the exact moment that the EH will be increased. Right?

However (and if the above are correct), I think that it's not so "bad" to say that an in-falling object that passes the EH increases the BH's mass. After all, this object is not able to escape any more and unavoidably will end up on the singularity. (I.e. this object "belongs" to the BH, although the actual increment of the BH's mass will be observed when it reaches the singularity).

So, concerning the example of the two BHs' merging (as detected by LIGO), we can assume that the new, larger EH (which formed after the merging) occurred when the two singularities (of the two original BHs) were merged. Is this correct?
What I mentioned in my previous post had to do with the bouncing that occurred after the merging of the two BHs. This bouncing lasted a small but finite time (detected by LIGO as a "ringdown signal" of about 0,05sec) and -after this- the new EH became again spherical. I think that this must happened via the gravitational waves at a speed c. Is that so?
That's why I thought that the increment of the EH should had occurred at a speed c (i.e. in order to get again a spherical EH).

Let's make a last effort to clarify these issues on this thread. If not then I'll start a new one.

 

[PAllen]

The question is: What is the exact moment that an outside observer can verify that the mass of a BH has been increased? I know that, essentially, all the mass of a BH is concentrated upon its singularity. So, I suppose that an actual increment of the BH's mass (as observed by an outside observer) occurs when the in-falling object reaches the singularity (i.e. when it is incorporated into the singularity). Is this what you mean?
And if this is correct, this is the exact moment that the EH will be increased. Right?
...

No, the event horizon is global feature of spacetime. The technical definition rendered into words is the boundary of events from which light cannot escape to (null) infinity. This has unusual consequences, including that as a body falls toward a BH, the horizon starts growing lopsidedly toward the infalling body even before it reaches the horizon. This can be seen heuristically from the definition: as the body approaches the horizon at near light speed, light from an event just outside the 'former' horizon in the direction of the body never makes it to infinity because its very slow outward progress leaves it captured as the infalling body crosses the horizon in the near future. Mathematically, it is well established that the exact location of the horizon can be affected by what happens arbitrarily far in the future.

 

[PeterDonis]

What is the exact moment that an outside observer can verify that the mass of a BH has been increased?

When the causal effects of whatever mass is falling into the BH reach him at the speed of light. In general this will depend on the details of the scenario (for a simple case, see below). My point is simply that whenever it turns out to be, it has no connection with when infalling matter crosses the EH, or with the "speed" at which the EH expands.

A simple case for which we do know the exact answer is this: imagine an observer hovering at some fixed altitude high above a non-rotating BH's event horizon, and a spherically symmetric shell of matter falling into the hole. The observer will be able to verify by observation that the mass has increased at the instant that the infalling shell of matter passes him. We can think of this as the infalling shell changing the spacetime geometry as it passes, from the geometry of vacuum surrounding an object of the original mass, to the geometry of vacuum surrounding an object of the new mass. That change is the causal effect of the infalling matter, and since the matter passes right by the observer, the observer sees the causal effect at the same time that the matter passes him--there is no delay for "travel time" because the causal effect is happening right where he is.

I suppose that an actual increment of the BH's mass (as observed by an outside observer) occurs when the in-falling object reaches the singularity (i.e. when it is incorporated into the singularity). Is this what you mean?

No, certainly not. See above.

 

[serp777]

In a sense, a BH event horizon is always moving at the speed of light, whether matter is falling in or not. More accurately, a trapping surface is the surface formed by ougoing null geodesics (light paths) that make no further 'progress'. In the classic, stable, BH, an event horizon is a trapping surface. As a result, all free fall observers 'observe' the event horizon passing at exactly c. More, any observer sees the event horizon pass at c - the same as outgoing light.

What you are describing is a coordinate dependent quantity which can be made pretty much whatever you want.

I'm confused on how a null surface, where light falls into the black hole, is moving at all. This is like saying that a shadow is moving; a shadow is just the lack of light though and doesn't exist in any physical sense.

 

[PeterDonis]

I'm confused on how a null surface, where light falls into the black hole

The event horizon is an outgoing null surface--it is made up of light rays that are moving outward, and are just at the boundary of escaping vs. not escaping to infinity. Light falling into the hole does not remain at the horizon; it falls right on past it into the hole's interior.

is moving at all

Any null surface is composed of light rays. Light rays are always moving, in the sense that any observer anywhere in any spacetime will always see light rays in his vicinity as moving at $c$; he will never see them as being at rest.

This is like saying that a shadow is moving

No, it is like saying that the light rays that define the shadow's boundary are moving.

 

[George K]

When the causal effects of whatever mass is falling into the BH reach him at the speed of light. In general this will depend on the details of the scenario (for a simple case, see below). My point is simply that whenever it turns out to be, it has no connection with when infalling matter crosses the EH, or with the "speed" at which the EH expands.

A simple case for which we do know the exact answer is this: imagine an observer hovering at some fixed altitude high above a non-rotating BH's event horizon, and a spherically symmetric shell of matter falling into the hole. The observer will be able to verify by observation that the mass has increased at the instant that the infalling shell of matter passes him. We can think of this as the infalling shell changing the spacetime geometry as it passes, from the geometry of vacuum surrounding an object of the original mass, to the geometry of vacuum surrounding an object of the new mass. That change is the causal effect of the infalling matter, and since the matter passes right by the observer, the observer sees the causal effect at the same time that the matter passes him--there is no delay for "travel time" because the causal effect is happening right where he is.
No, certainly not. See above.

Thanks for your reply. I had also thought the scenario of the "spherically symmetric shell of matter falling into the hole", as this is a scenario where no bouncing of the EH will occur (of course in the case of an ideally spherical and homogeneous shell of matter).
I think that (at least) I was right about the bouncing of the EH that occurs when a large object falls into the BH (as in the case of the two BHs merging detected by LIGO). I mean that the geometrical re-arrangement (so that the EH will become again spherical) will take place via the gravitational waves (i.e. at a speed c). Please, confirm.

 

[George K]

No, the event horizon is global feature of spacetime. The technical definition rendered into words is the boundary of events from which light cannot escape to (null) infinity. This has unusual consequences, including that as a body falls toward a BH, the horizon starts growing lopsidedly toward the infalling body even before it reaches the horizon. This can be seen heuristically from the definition: as the body approaches the horizon at near light speed, light from an event just outside the 'former' horizon in the direction of the body never makes it to infinity because its very slow outward progress leaves it captured as the infalling body crosses the horizon in the near future. Mathematically, it is well established that the exact location of the horizon can be affected by what happens arbitrarily far in the future.

I think that you mean (in simple words) that the gradual increment of the BH's spacetime curvature -caused by an infalling object- will not let the light of an "event just outside of the EH" to escape, even before this object reaches the EH. Is this correct? (Please confirm.)

 

[PeterDonis]

I mean that the geometrical re-arrangement (so that the EH will become again spherical) will take place via the gravitational waves (i.e. at a speed c).

Yes, that's correct. But that still is not the same thing as "the rate at which the EH expands", nor does it mean that outside observers see the hole's mass increase when infalling matter crosses the horizon. They see the hole's mass increase when the effect of the infalling matter propagates to them at $c$. That effect is not limited to the "rearrangement of the horizon"; infalling matter has effects on spacetime curvature wherever it is. In the case of merging black holes, as seen from far away, the system composed of the two original black holes has mass equal to the sum of their masses; but the final, merged black hole, after all gravitational waves have propagated away and the final horizon is symmetrical, has a mass less than that--so an observer far away would see the mass of the system decrease as the outgoing gravitational waves passed him. In all cases, changes in spacetime curvature propagate at $c$.

 

[PAllen]

I think that you mean (in simple words) that the gradual increment of the BH's spacetime curvature -caused by an infalling object- will not let the light of an "event just outside of the EH" to escape, even before this object reaches the EH. Is this correct? (Please confirm.)

Yes (in simple words).

 

[George K]

Yes, that's correct. But that still is not the same thing as "the rate at which the EH expands", nor does it mean that outside observers see the hole's mass increase when infalling matter crosses the horizon. They see the hole's mass increase when the effect of the infalling matter propagates to them at $c$. That effect is not limited to the "rearrangement of the horizon"; infalling matter has effects on spacetime curvature wherever it is. In the case of merging black holes, as seen from far away, the system composed of the two original black holes has mass equal to the sum of their masses; but the final, merged black hole, after all gravitational waves have propagated away and the final horizon is symmetrical, has a mass less than that--so an observer far away would see the mass of the system decrease as the outgoing gravitational waves passed him. In all cases, changes in spacetime curvature propagate at $c$.

Thank you for your reply. Unfortunately, at first, I was confused but now the whole issue is perfectly clear.

 

[George K]

Yes (in simple words).

That was very interesting. Thanks.