[DoctorBeaver]

Update on my pondering.

Light cannot escape from an EH, so the escape velocity is >c. But if an object free-falls across an EH, what is its velocity? I don't see that it necessarily has to be relativistic (That would be especially true of supermassive BHs).

What if the object were approaching the EH at an angle? Wouldn't the angle of approach have some bearing on how fast it was receding from distant objects and, hence, the resultant red shift (objects at 90^o would hardly have any red shift)?

And that makes me ponder a different aspect of the question. If you approached the EH at an angle, wouldn't the light from behind you be shifted differently from that ahead of you?

Actually, that would be the case no matter what your angle of approach; objects at 90^o would have no shift either way.

Sorry if my thoughts are a bit haphazard, that's just the way I think about things.

[LeeE]

Do you mean like 2 cones base to base? That's what I was thinking.

It wouldn't necessarily result in a symmetry along its time axis, though. Imagine the case of a cone the entire base of which intersects the EH at an angle. At the EH the cone would invert with its apex at the singularity.

Sort of - because the cone would be in a gradient, the base would have to contract towards a point as it approached the singularity but I would imagine the sides of the cone to be smoothly curved and it would end up as a sort of elongated egg-shape, but with pointed ends instead of rounded ones.

There wouldn't be true symmetry along the time axis, of course, because the axis is directional, but the shape of the cone would approach symmetry along that axis.  All I think it actually signifies is that in such a situation there's only one possible future, which we know already:)  It does seem like quite a nice way to illustrate it though.

[DoctorBeaver]

Do you mean like 2 cones base to base? That's what I was thinking.

It wouldn't necessarily result in a symmetry along its time axis, though. Imagine the case of a cone the entire base of which intersects the EH at an angle. At the EH the cone would invert with its apex at the singularity.

Sort of - because the cone would be in a gradient, the base would have to contract towards a point as it approached the singularity but I would imagine the sides of the cone to be smoothly curved and it would end up as a sort of elongated egg-shape, but with pointed ends instead of rounded ones.

A fat, pointy-ended sausage!  []

All I think it actually signifies is that in such a situation there's only one possible future, which we know already

Indeed. Until the entire base of the cone intersects the EH, all possible futures are still options. But when it does - SCHLOOOOOP!

heh - can we say that the diminishing fatness of the sausage depends on the schloooopiness of the BH? Imagine presenting that in a paper! []

[graham.d]

Light cannot escape from an EH, so the escape velocity is >c. But if an object free-falls across an EH, what is its velocity? I don't see that it necessarily has to be relativistic (That would be especially true of supermassive BHs).

If you fell in from a long way off it would be relativistic. The definition of the event horizon is the surface from which the escape velocity equals the speed of light - ergo, if falling from an infinite distance (by symmetry) you would just achieve this speed at the EH. This is not allowed by special relativity but it means that the universe would have Lorentz contracted in your direction of travel considerably and the BH's mass would be even higher relative to you. There was a paper some years ago which showed what objects would look like if you were passing them at relativistic speeds; the results were not what you would expect intuitively, and this was just Special Relativity. As I said before, this needs a lot of maths work to glean insight.

[LeeE]

I think that using escape velocities might actually be confusing the issue here.

An escape velocity is the initial speed that when imparted to an object is sufficient to overcome an opposite acceleration due to gravity so that it will end up infinitely far away, with infinitely small speed.

In the case of a BH, the EH marks the point along the gravity gradient from the BH where the escape velocity from the BH is equal to c, so nothing within an EH can escape it by being given a sufficient initial velocity, because nothing can be imparted with a speed > c.

However, this doesn't mean that anything located at the EH, or even within it, has to be travelling at c.  For example, on the surface of the Earth, the escape velocity is about 11200 m/s but none of us actually on the surface of the Earth is travelling at that speed, so you wouldn't necessarily need to be travelling at c when you cross the EH and you should be able to still see the universe outside.  The light falling into the BH will be blue-shifted but as you accelerate towards the singularity the light will appear to be more and more red-shifted until you reach the point where your velocity approaches c and the apparent energy of the light reaching you approaches zero.

[DoctorBeaver]

In the case of a BH, the EH marks the point along the gravity gradient from the BH where the escape velocity from the BH is equal to c, so nothing within an EH can escape it by being given a sufficient initial velocity, because nothing can be imparted with a speed > c.

My mistake. I should have put =c rather than >c.

The light falling into the BH will be blue-shifted but as you accelerate towards the singularity the light will appear to be more and more red-shifted until you reach the point where your velocity approaches c and the apparent energy of the light reaching you approaches zero.

I did wonder about that, and that's what prompted my other thread about wave stretching. You've made me think that maybe I'm not a total dork after all  []

[LeeE]

Do you mean like 2 cones base to base? That's what I was thinking.

It wouldn't necessarily result in a symmetry along its time axis, though. Imagine the case of a cone the entire base of which intersects the EH at an angle. At the EH the cone would invert with its apex at the singularity.

Sort of - because the cone would be in a gradient, the base would have to contract towards a point as it approached the singularity but I would imagine the sides of the cone to be smoothly curved and it would end up as a sort of elongated egg-shape, but with pointed ends instead of rounded ones.

A fat, pointy-ended sausage!  []

All I think it actually signifies is that in such a situation there's only one possible future, which we know already

Indeed. Until the entire base of the cone intersects the EH, all possible futures are still options. But when it does - SCHLOOOOOP!

heh - can we say that the diminishing fatness of the sausage depends on the schloooopiness of the BH? Imagine presenting that in a paper! []

Hmm... fat pointy-ended sausages being drawn into a BH - just my base sense of humour but I can't help remembering a certain phrase concerning a fan and something that hit it.

[DoctorBeaver]

Do you mean like 2 cones base to base? That's what I was thinking.

It wouldn't necessarily result in a symmetry along its time axis, though. Imagine the case of a cone the entire base of which intersects the EH at an angle. At the EH the cone would invert with its apex at the singularity.

Sort of - because the cone would be in a gradient, the base would have to contract towards a point as it approached the singularity but I would imagine the sides of the cone to be smoothly curved and it would end up as a sort of elongated egg-shape, but with pointed ends instead of rounded ones.

A fat, pointy-ended sausage!  []

All I think it actually signifies is that in such a situation there's only one possible future, which we know already

Indeed. Until the entire base of the cone intersects the EH, all possible futures are still options. But when it does - SCHLOOOOOP!

heh - can we say that the diminishing fatness of the sausage depends on the schloooopiness of the BH? Imagine presenting that in a paper! []

Hmm... fat pointy-ended sausages being drawn into a BH - just my base sense of humour but I can't help remembering a certain phrase concerning a fan and something that hit it.

What are you insinuating, young man?  Or are you just being coarse? [!]

[graham.d]

Hmm. The escape velocity is the velocity at the surface (in this case the EH) at which you have suficient energy to escape (just) to infinity. Consequently, if you start from infinity and just fall under the gravity of the object, you will achieve this velocity at this surface. In practice we are talking about just fairly large distances; it is just that infinity makes the calculations a bit easier, but the principle is the same. As I said before, if somehow you could use retro rockets to slow yourself down this would not apply, but you would still have a huge velocity. In an oblique entry you would probably end up in a decaying orbit into the BH. I am unsure how the universe would look in this case. Well, I am unsure in every case actually.

[LeeE]

I did not intend to Insinuate anything - It is purely my coarse sense of humour.

However, were one to find oneself in such a situation (and assuming that one didn't want to be in it) I think that it's quite possible that some folk, obviously less cultured and refined than yourself, might actually use the phase I alluded to, but without realising how literally appropriate it might actually be, especially if the BH has any angular momentum.

[DoctorBeaver]

I did not intend to Insinuate anything - It is purely my coarse sense of humour.

However, were one to find oneself in such a situation (and assuming that one didn't want to be in it) I think that it's quite possible that some folk, obviously less cultured and refined than yourself, might actually use the phase I alluded to, but without realising how literally appropriate it might actually be, especially if the BH has any angular momentum.

Ah yes, I can see the analogy.