The discussion revolves around the concept of the event horizon (EH) of a black hole and the assertion that it is expanding at the speed of light (c). Participants explore the implications of this claim, questioning its justification and the nature of the EH in relation to observers and physical laws. The conversation touches on theoretical aspects of relativity, observer perspectives, and the semantics of motion in the context of black holes.
Participants express differing views on the nature of the EH and its motion. While some agree on certain aspects of the EH's behavior, there is no consensus on the justification for claiming that the EH is expanding at c or the implications of this claim.
Participants note that the discussion involves complex concepts in relativity, including the classification of velocities as timelike, spacelike, or lightlike, and the implications of these classifications for the EH. There are unresolved questions about the nature of the EH and its relationship to observers, as well as the mathematical underpinnings of the claims made.
Tracer said: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.What is the EH expanding in reference to?
Bill_K said: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 said: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 said: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 said: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 said: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?
Tracer said:DrGreg said: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.
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.Tracer said: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?
DaleSpam said: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 said: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?
Nugatory said: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 said:There are several other concepts which could explain the behavior of objects at the event horizon.
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.Tracer said: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.
In reference to any inertial frame. That is what it means for something to be frame-invariant.Tracer said: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?
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.Tracer said:How does the event horizon qualify as an object?
Yes.Tracer said:(1) The EH of a BH occurs at a radial distance from a mass where the escape velocity is c.
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".Tracer said:(2) Any object trying to move radially outward from and at an event horizon at c will remain at the EH.
Yes, in any local inertial frame.Tracer said:(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.
I already answered that. It is lightlike, so it moves at c in a coordinate-independent (aka frame-invariant) sense.Tracer said:Why is it the consensus that the EH has a velocity vector of c radially outward from the BH? what suports that 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 said:Why was the concept of the event horizon moving radially outwards at c the favored consensus?
Nugatory said: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.
Tracer said:This forum forbids the discussion of speculative topics. Would you accept an answer by email?
Tracer said:This forum forbids the discussion of speculative topics. Would you accept an answer by email?
I agree. Learn the standard before examining the wackos. Plus, the question has been answered.Nugatory said: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?
Nugatory said:---- Do you understand what GR says about the experience of the two observers I described above?
DaleSpam said:I agree. Learn the standard before examining the wackos. Plus, the question has been answered.
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.Tracer said: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 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.)Tracer said: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.
Tracer said: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.
PAllen said: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.