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

1. Mar 1, 2013

### 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?

2. Mar 1, 2013

### Staff: Mentor

An inertial observer close to it.

3. Mar 1, 2013

### Bill_K

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.

4. Mar 1, 2013

### Tracer

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?

5. Mar 1, 2013

### PAllen

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.

6. Mar 1, 2013

### Tracer

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?

7. Mar 1, 2013

### 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.

8. Mar 1, 2013

### PAllen

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.

9. Mar 1, 2013

### Tracer

10. Mar 1, 2013

### PAllen

Last edited: Mar 1, 2013
11. Mar 1, 2013

### Staff: Mentor

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.

12. Mar 2, 2013

### Tracer

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 beleive 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?

13. Mar 2, 2013

### someGorilla

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

14. Mar 2, 2013

### Staff: Mentor

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.

15. Mar 2, 2013

### Tracer

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 concensus over other concepts? Obviously those in favor of the consensus thought it to be the most sensable concept, but why?

16. Mar 2, 2013

### Staff: Mentor

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 Schwarzchild 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.

17. Mar 2, 2013

### Staff: Mentor

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.

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

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.

Yes.

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".

Yes, in any local inertial frame.

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

18. Mar 2, 2013

### Staff: Mentor

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.

19. Mar 2, 2013

### Tracer

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

20. Mar 2, 2013

### Staff: Mentor

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?

Last edited: Mar 2, 2013