Why is the EH of a BH considered to be expanding at c?

[Tracer]

The comment, "The Event Horizon is expanding at the speed of light", has been used in posts in this forum. What is the justification or reason for the comment? It seems contadictory that a fixed EH radius could be moving. What is the EH expanding in reference to?

 

[Nugatory]

What is the EH expanding in reference to?

An inertial observer close to it.

 

[Bill_K]

What is the EH expanding in reference to?

It isn't really "expanding" in the sense of getting any larger. But all local observers at r = 2m fall inward (that is, r decreases). The only exception being the limiting case - a light ray heading outward, which remains at r = 2m.

 

[Tracer]

It isn't really "expanding" in the sense of getting any larger. But all local observers at r = 2m fall inward (that is, r decreases). The only exception being the limiting case - a light ray heading outward, which remains at r = 2m.

I can agree with that. However my first question remains unanswered. What justification is there for claiming in any sense that the event horizon is expanding at the rate of c?

 

[PAllen]

I can agree with that. However my first question remains unanswered. What justification is there for claiming in any sense that the event horizon is expanding at the rate of c?

Every observer crossing the horizon experiences it going past them at c. Every local inertial frame spanning the horizon has it going 'outwards' at c.

 

[Tracer]

Every observer crossing the horizon experiences it going past them at c. Every local inertial frame spanning the horizon has it going 'outwards' at c.

Since these experiences can't be comfirmed by actual measurements, I wonder if their acceptance as truth is based on speculation on how trying to move outward from an event horizon at c results only in remaining stationary relative to the horizon. Or is there mathematical proof that the stated experiences are correct?

 

[DrGreg]

If an apple falls to the Earth's surface and hits it at 5 m/s, then, relative to the apple, the ground is moving upwards at 5 m/s.

It's the same with a black hole except that event horizons always "hit" apples (or anything else with non-zero mass) at the speed of light instead of 5 m/s.

 

[PAllen]

Since these experiences can't be comfirmed by actual measurements, I wonder if their acceptance as truth is based on speculation on how trying to move outward from an event horizon at c results only in remaining stationary relative to the horizon. Or is there mathematical proof that the stated experiences are correct?

1) Sure they can. The light from each prior object passing the horizon is the horizon visually. This light going by is like any other light to the infaller - it goes by at c.

2) There is mathematical proof.

 

[Tracer]

If an apple falls to the Earth's surface and hits it at 5 m/s, then, relative to the apple, the ground is moving upwards at 5 m/s.

I agree, but nobody would ever say that while they were in free fall from that apple tree that the radius of the Earth was expanding.

It's the same with a black hole except that event horizons always "hit" apples (or anything else with non-zero mass) at the speed of light instead of 5 m/s.

If an object free falls from infinity into a black hole, it is just a matter of semantics as to whether the object hits the event horizon at c or the event horizon hits the object at c. But either way the radius of the horizon is not increasing. Most of the moving is being done by the free falling object.
But what if the object is a ship that has used all of its fuel to reduce its RV with the horizon to very close to zero just befor it reaches the horizon. The ship then free falls through the horizon. Arguments aside on what hits what. At what speed would the hitting occur?

 

[PAllen]

If an apple falls to the Earth's surface and hits it at 5 m/s, then, relative to the apple, the ground is moving upwards at 5 m/s.

I agree, but nobody would ever say that while they were in free fall from that apple tree that the radius of the Earth was expanding.

It's the same with a black hole except that event horizons always "hit" apples (or anything else with non-zero mass) at the speed of light instead of 5 m/s.

If an object free falls from infinity into a black hole, it is just a matter of semantics as to whether the object hits the event horizon at c or the event horizon hits the object at c. But either way the radius of the horizon is not increasing. Most of the moving is being done by the free falling object.
But what if the object is a ship that has used all of its fuel to reduce its RV with the horizon to very close to zero just befor it reaches the horizon. The ship then free falls through the horizon. Arguments aside on what hits what. At what speed would the hitting occur?

Agreed that 'expanding' is not the the most precise statement. Passing at c is accurate.

It is not semantics as to what is moving at c, for the horizon. There is no local inertial frame where the the infaller is moving at c. Conversely, there is no local inertial frame, at all, where the horizon is moving at anything other than c. For the infaller, in their local inertial rest frame, they are at rest, not moving at all.

As for your rocket hovering in picometer above the horizon, then running out of fuel, the horizon still passes at exactly c for the rocket.

Please note: in every local inertial frame that includes the horizon, the horizon moves at c.

 

[Dale]

However my first question remains unanswered. What justification is there for claiming in any sense that the event horizon is expanding at the rate of c?

In relativity a vector can be timelike, spacelike, or lightlike. The velocity of a massive particle (v<c) is timelike, and the velocity of a massless particle (v=c) is lightlike. Different frames may disagree about a massive particle's velocity, but they all agree about the classification as timelike or lightlike. I.e. Being timelike or lightlike is a frame invariant fact.

The event horizon is lightlike.

 

[Tracer]

In relativity a vector can be timelike, spacelike, or lightlike. The velocity of a massive particle (v<c) is timelike, and the velocity of a massless particle (v=c) is lightlike. Different frames may disagree about a massive particle's velocity, but they all agree about the classification as timelike or lightlike. I.e. Being timelike or lightlike is a frame invariant fact.

The event horizon is lightlike.

I appreciate the responses and patience of those who have provided aswers to to my questions regarding the motion of the event horizon relative to an observer free falling through it. I am not being deliberately obtuse, nor do I want to be argumenative. However, I still have not had an epiphony regarding the subject. Your statement that the event horizon is lightlike seems to imply that all massless objects move at the speed of light in reference to something, but what? How does the event horizon qualify as an object?

Here are some things I believe to be true regarding the event horizon. Are they correct?
(1) The EH of a BH occurs at a radial distance from a mass where the escape velocity is c.
(2) Any object trying to move radially outward from and at an event horizon at c will remain at the EH.
(3) If for any reason the motion vector of an event horizon is radially outward at c, then any object falling toward the event horizon at any speed will pass through the EH at c because of how relativistic velocities are added.

Why is it the consensus that the EH has a velocity vector of c radially outward from the BH? what suports that consensus? Are there other possibilities for what happens at the horizon?

 

[someGorilla]

Don't you see that your point 2) is exactly equivalent to saying that the event horizon moves at c?

 

[Nugatory]

Why is it the consensus that the EH has a velocity vector of c radially outward from the BH? what supports that consensus? Are there other possibilities for what happens at the horizon?

We are not just saying that the EH has a velocity vector of c radially outwards (although if you're not trying to think in terms of a curved four-dimensional spacetime it would be easy to think that). You have to ask yourself "velocity relative to WHAT?" and "In curved spacetime, is expansion the same thing as the radius increasing?" and "just what do you mean by 'radius', if there's a singularity in any straight line drawn through the 'center' of the black hole?"

I suspect that you're thinking in terms of the perspective of an observer far away from the black hole. This observer may reasonably consider the event horizon to a spherical surface of constant size, so this notion that it is "expanding" makes no sense. But if you consider the perspective of an observer near to or falling through the event horizon the most sensible view is that the event horizon is indeed moving radially outwards - read your point #2 again carefully.

 

[Tracer]

But if you consider the perspective of an observer near to or falling through the event horizon the most sensible view is that the event horizon is indeed moving radially outwards - read your point #2 again carefully.

There are several other concepts which could explain the behavior of objects at the event horizon. Why was the concept of the event horizon moving radially outwards at c the favored consensus? What factors favored this consensus over other concepts? Obviously those in favor of the consensus thought it to be the most sensable concept, but why?

 

[Nugatory]

There are several other concepts which could explain the behavior of objects at the event horizon.

At the risk of answering a question with a question... Can you give an example?

Consider two observers, very near to one another, one using powerful rockets to maintain a constant Schwarzschild r coordinate just outside the horizon and the other passing by at a high relative velocity as he free-falls in from infinity... And remember that neither can directly observe the event horizon, all they can do is make statements about the behavior of light coming at them from various directions.

 

[Dale]

I appreciate the responses and patience of those who have provided aswers to to my questions regarding the motion of the event horizon relative to an observer free falling through it. I am not being deliberately obtuse, nor do I want to be argumenative. However, I still have not had an epiphony regarding the subject.

Are you familiar with four-vectors and Minkowski spacetime? If not, then you should start there. It is hard to learn if you skip concepts.

Your statement that the event horizon is lightlike seems to imply that all massless objects move at the speed of light in reference to something, but what?

In reference to any inertial frame. That is what it means for something to be frame-invariant.

How does the event horizon qualify as an object?

It doesn't. It is a lightlike surface, not an object. However, it is still lightlike, regardless of the fact that it is not an object.

(1) The EH of a BH occurs at a radial distance from a mass where the escape velocity is c.

Yes.

(2) Any object trying to move radially outward from and at an event horizon at c will remain at the EH.

Yes, although nothing that I would call "an object" can move at c. I only use the term "an object" to refer to massive objects. I wouldn't consider something made of light to be "an object".

(3) If for any reason the motion vector of an event horizon is radially outward at c, then any object falling toward the event horizon at any speed will pass through the EH at c because of how relativistic velocities are added.

Yes, in any local inertial frame.

Why is it the consensus that the EH has a velocity vector of c radially outward from the BH? what suports that consensus?

I already answered that. It is lightlike, so it moves at c in a coordinate-independent (aka frame-invariant) sense.

 

[Dale]

Why was the concept of the event horizon moving radially outwards at c the favored consensus?

The primary factor is that it is a coordinate-independent description. Coordinate-independent facts are generally considered to be more physically relevant than coordinate-dependent ones.

 

[Tracer]

At the risk of answering a question with a question... Can you give an example?
One example involves the expansion of space at the rate of c at an event horizon.
A second example involves an etherist theory of flowing space.
I would like to see a debunking of those examples but those topics are taboo in this forum.

Consider two observers, very near to one another, one using powerful rockets to maintain a constant Schwarzschild r coordinate just outside the horizon and the other passing by at a high relative velocity as he free-falls in from infinity... And remember that neither can directly observe the event horizon, all they can do is make statements about the behavior of light coming at them from various directions.

This forum forbids the discussion of speculative topics. Would you accept an answer by email?

 

[Nugatory]

This forum forbids the discussion of speculative topics. Would you accept an answer by email?

Maybe one of the moderators will chime in, but my experience has been that "I know this isn't right, but I don't know why... Where am I going wrong and what is the accepted answer?" usually survives moderation. It's the people who are more interested in pushing their own speculation than listening who get (rightly) shut down.

There is little reason to consider "expansion of space" or an "etherist theory" until after thoroughly understanding the general relativity explanation - we can't say that the GR explanation is wanting without understanding it. Do you understand what GR says about the experience of the two observers I described above?

 

[PAllen]

This forum forbids the discussion of speculative topics. Would you accept an answer by email?

You suggested:

----
One example involves the expansion of space at the rate of c at an event horizon.
A second example involves an etherist theory of flowing space.
------

both of these can lead to the same predictions as GR, thus both are still require motion of the horizon at c in the sense I described (which focuses on the physics):

Every possible inertial observer (whatever their relative motion to each other) whose world line crosses the horizon sees it go by at c (and this can be seen in the sense that light emitted by prior infallers on horizon crossing can be seen). Such light is indistinguishable from any other light going by (e.g. moment before or after). I also explained (and you completely ignored) that an infaller starting from static position at one picometer above the horizon, then falling through, sees it go by at c.

In short, every observer who can see the horizon (by virtue of light of prior infallers) sees it go by at c, indistinguishable from any other light they have seen.

The statements above are observations, independent of any interpretations. If you prefer to think of these observations with a different mental model that is fine. However, you can certainly see that the horizon moving radially at c is the only natural point of view for any observer crossing the horizon, considering their own rest frame.

 

[Dale]

There is little reason to consider "expansion of space" or an "etherist theory" until after thoroughly understanding the general relativity explanation - we can't say that the GR explanation is wanting without understanding it. Do you understand what GR says about the experience of the two observers I described above?

I agree. Learn the standard before examining the wackos. Plus, the question has been answered.

 

[Tracer]

---- Do you understand what GR says about the experience of the two observers I described above?

This is my understanding.
The astronaut hovering close to the event horizon would consider himself to be in an motionless IRF being subjected to an intense gravitational field. He would see the doppler shift and angles of incomming light from the universe as affected by the perceived gravitational field. He would see light from stars and galaxies as if they were moved to positions more back and opposite of the source of the perceived gravitational field. Light would be blue shifted from those sources. Light coming from the direction of the black hole would be red shifted.

The astronaut who is free falling close to the event horizon would consider himself to be in an gravity free IRF that is moving at a relative velocity of nearly c with the rest of the universe. He would see the doppler shifts and angles of incomming light as affected by his perceived relative velocity those light sources. Light sources from behind him would be red shifted and light sources ahead of him would be blue shifted. He would see light from stars and galaxies as if they were moved to positions more forward in his direction of motion.

 

[Tracer]

I agree. Learn the standard before examining the wackos. Plus, the question has been answered.

Wackos? I suppose that says it all. Your answers have been helpful and I have appreciated them.
Regards, Tracer

 

[PAllen]

This is my understanding.
The astronaut hovering close to the event horizon would consider himself to be in an motionless IRF being subjected to an intense gravitational field.

No, according to GR this frame would be extremely non-inertial. In GR, inertial frames are exclusively free fall frames. Only locally, in inertial frames, can you talk about a universal light speed. In non-inertial frames, or over long distances in GR, you cannot talk about light always going c.

He would see the doppler shift and angles of incomming light from the universe as affected by the perceived gravitational field. He would see light from stars and galaxies as if they were moved to positions more back and opposite of the source of the perceived gravitational field. Light would be blue shifted from those sources. Light coming from the direction of the black hole would be red shifted.

The astronaut who is free falling close to the event horizon would consider himself to be in an gravity free IRF that is moving at a relative velocity of nearly c with the rest of the universe.

He would consider himself at rest in his own inertial rest frame. Speed relative to distant objects is complex, interpreted quantity with no invariant definition in GR. In particular, If this free faller dropped from hovering just outside the horizon, they would not see any substantial change in the appearance of the rest of the universe (behind them) as they crossed the horizon. In particular, there would be no sudden increase in blue shift that could be interpreted as a rapid increase in speed of distant objects. None the less, they would see the horizon go by at c (and I have explained several times in what sense you can talk about seeing the horizon.)

He would see the doppler shifts and angles of incomming light as affected by his perceived relative velocity those light sources. Light sources from behind him would be red shifted and light sources ahead of him would be blue shifted. He would see light from stars and galaxies as if they were moved to positions more forward in his direction of motion.

Your last description is somewhat true of a free faller from infinity. It is not true at all for a free faller starting from hovering just above the horizon. For them, stars behind them would be blue shifted, not red shifted. This blue shift would be present while hovering, and would not change significantly when they stopped hovering and the horizon passed them. As for in front of them, they wouldn't see stars on the other side of the BH at all. They would see light from earlier infalling matter as it was just before horizon crossing; finally as it was at horizon crossing when they crossed the horizon.

 

[Tracer]

No, according to GR this frame would be extremely non-inertial. In GR, inertial frames are exclusively free fall frames. Only locally, in inertial frames, can you talk about a universal light speed. In non-inertial frames, or over long distances in GR, you cannot talk about light always going c.

He would consider himself at rest in his own inertial rest frame. Speed relative to distant objects is complex, interpreted quantity with no invariant definition in GR. In particular, If this free faller dropped from hovering just outside the horizon, they would not see any substantial change in the appearance of the rest of the universe (behind them) as they crossed the horizon. In particular, there would be no sudden increase in blue shift that could be interpreted as a rapid increase in speed of distant objects. None the less, they would see the horizon go by at c (and I have explained several times in what sense you can talk about seeing the horizon.)


Your last description is somewhat true of a free faller from infinity. It is not true at all for a free faller starting from hovering just above the horizon. For them, stars behind them would be blue shifted, not red shifted. This blue shift would be present while hovering, and would not change significantly when they stopped hovering and the horizon passed them. As for in front of them, they wouldn't see stars on the other side of the BH at all. They would see light from earlier infalling matter as it was just before horizon crossing; finally as it was at horizon crossing when they crossed the horizon.

The issue of a moving/expanding event horizon has been resolved as far as I am concerned. Thank you for your patience.
I was wrong to identify the hovering astronaut's reference frame as inertial. I understand the effects you mention for the astronaut who stops hovering and then falls through the horizon.
Regards, Tracer