Can Energy Really Exist on the Surface of a Black Hole?

[yoron]

Passionflower, you wrote "However for a static observer near the event horizon radial distance, and thus volume as well, does increase without bound."

A static observer is one hovering aka accelerating here right?
So, to this static observer it would indeed be possible to 'pack' stuff?

I'm getting a little confused thinking about it, as I see it as 'local time' for a infalling observer should be 'as usual', allowing him to traverse any other persons 'apparent Event horizon' in some for him definable time, according to his frame of reference.

So this place expanding without bounds for our static observer near/at the Event horizon, is that a direct effect of his hovering, and how would he describe a infalling observer? Although I think you are correct, as the 'expanding effect' should be as well outside the EV as inside I can't help wonder how the hovering observer then would describe the infalling.
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The infalling observer would not be moving at all, would he? And what about blue/redshift measured relative the infalling observer? Although the light should be blue shifted for our static observer as I think of it, what about the expansion of distance? And, would the infalling observer then be 'stretched' relative the static/hovering? And what about if we change 'frame' to the infalling, observing the static/hovering observer?
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The thing is, if I assume that the 'expanding effect' is valid for both the infalling, as well as for the hovering, then the assumption I make of him passing any Event Horizon seem questionable? Which then indeed makes it possible to assume a infinite amount of mass coagulating around the Event Horizon, from all perspectives?

 

[skeptic2]

Does no one have a problem with changes in the black hole's gravity violating causality.

While a static gravitational field may be considered just a distortion of spacetime, changes in the gravitational field such as the aggregation of additional matter must propagate from inside the EH to the outside. It is assumed that there would be a slight but detectable difference in the gravitational field of a BH between its gravitational field before matter crosses the EH and after. The problem is that if the singularity is in the future for everything inside the EH, the EH must be in its past. Any change in the gravitational field from inside the EH would have to propagate backwards in time.

 

[Dale]

Does no one have a problem with changes in the black hole's gravity violating causality.

While a static gravitational field may be considered just a distortion of spacetime, changes in the gravitational field such as the aggregation of additional matter must propagate from inside the EH to the outside. It is assumed that there would be a slight but detectable difference in the gravitational field of a BH between its gravitational field before matter crosses the EH and after. The problem is that if the singularity is in the future for everything inside the EH, the EH must be in its past. Any change in the gravitational field from inside the EH would have to propagate backwards in time.

Causality violations are a known feature of GR, but I am not sure that this is an example. What is the metric for an aggregating black hole and what feature of that metric do you consider to be backwards causality?

 

[PeterDonis]

While a static gravitational field may be considered just a distortion of spacetime, changes in the gravitational field such as the aggregation of additional matter must propagate from inside the EH to the outside.

What makes you think this? The change in the gravitational field propagates from the additional matter that falls in, just as in the original formation of the black hole from a collapsing object, the gravitational field of the black hole propagates from the collapsing object. Nothing has to propagate from inside the EH.

 

[Passionflower]

Nothing much at all? Taking out my pocket calculator, I divide 0.00864134 by 0.00000314 and obtain 2752.02 - the ratio of volumes. [More precisely - I presume what we mean by volume here is the differential volume between two spherical surfaces having radii between r and r+dr, at 1mm above the 'EH'.

Yes but not r and r+0.001, the r value is actually smaller than r+0.001. r does not represent a distance for stationary objects.

And try 0.1mm, 0.01mm, etc - trend is towards infinity as we all well know.

The ratio tends to infinity but not the volume because even though the volume is always larger than the Euclidean value it does decrease with smaller radii and eventually becomes zero as well.

And btw since I was taken to task in another thread for assuming radial distance can have some kind of 'normal' meaning in SC's, what and how do you define 1mm radial distance here, given the circular nature of defining such things? Can you logically escape the '(differential volume)/(differential surface area)' bind?

I am not sure what you mean here. I simply take the volume between two shells, one shell at the event horizon and the other 1 millimeter above it.

And this is not a contradiction of the earlier remarks 'but it is not that much more.' ...'So it is really nothing dramatic.'?

It is certainly very far removed from infinite volume.

However for a static observer near the event horizon radial distance, and thus volume as well, does increase without bound.

Oops, sorry my brain was somewhere else when I added that. It is not correct and actually in contradiction with what I wrote above.

Please ignore this comment.

 

[Q-reeus]

I am not sure what you mean here. I simply take the volume between two shells, one shell at the event horizon and the other 1 millimeter above it.

OK thanks that clears up what volume actually means here - I had a somewhat different picture.

Please ignore this comment.

I have often wished for the same - consider it done.

 

[yoron]

Wasn't gravity a geometry in Einstein's definitions? If it is so there should be nothing hindering gravity's potential inside a Event Horizon to 'attract' the outside, as I think of it? As for exchanging time for space? Isn't that depending on what definitions you use?

And okay Passion flower, but I still think you made sense, although I'm not sure how much it would seem to expand for a 'static observer'? Infinite seems somewhat much, but shouldn't there be a equivalence at the Event Horizon to something moving close to the speed of light? if we define it as the place where all light 'disappear', having only one path left to take.

 

[skeptic2]

Wasn't gravity a geometry in Einstein's definitions? If it is so there should be nothing hindering gravity's potential inside a Event Horizon to 'attract' the outside, as I think of it?.

I wasn't suggesting that there was something hindering gravity's potential inside an Event Horizon to "attract" the outside, I was suggesting that CHANGES in the gravitational field would have to propagate backwards in time to be felt outside the EH.

The logic is simple - if nothing passes event horizon of some hypothetical seed black hole then it can't grow it's mass and expand it's EH.

If matter passes through the EH, the increase in the gravitational field would have to travel backwards in time to reach the EH. So ironically matter falling through the EH would not cause the BH to grow. Only matter remaining outside the EH can increase the size of the BH.

 

[Dale]

I was suggesting that CHANGES in the gravitational field would have to propagate backwards in time to be felt outside the EH.

I think that is an assumption, which you have not yet justified.

 

[PeterDonis]

I wasn't suggesting that there was something hindering gravity's potential inside an Event Horizon to "attract" the outside, I was suggesting that CHANGES in the gravitational field would have to propagate backwards in time to be felt outside the EH.

If matter passes through the EH, the increase in the gravitational field would have to travel backwards in time to reach the EH. So ironically matter falling through the EH would not cause the BH to grow. Only matter remaining outside the EH can increase the size of the BH.

The "gravity" that is felt outside the BH is not "propagated" from inside the BH. Objects move according to the curvature of spacetime locally, not at a distance, so whatever curvature of spacetime is already there outside the BH is what is felt as the "gravity" of the BH.

The curvature of spacetime outside a BH is not "propagated" from inside the BH. In so far as a stationary field is "propagated" at all, the field outside a BH is propagated, as I said before, from the matter that originally collapsed to create the BH. And if the mass of the BH changes as a result of more matter falling in, the change in the field outside the BH is propagated from the additional matter that falls in.

 

[Constantin]

The "gravity" that is felt outside the BH is not "propagated" from inside the BH. Objects move according to the curvature of spacetime locally, not at a distance, so whatever curvature of spacetime is already there outside the BH is what is felt as the "gravity" of the BH.

The curvature of spacetime outside a BH is not "propagated" from inside the BH. In so far as a stationary field is "propagated" at all, the field outside a BH is propagated, as I said before, from the matter that originally collapsed to create the BH. And if the mass of the BH changes as a result of more matter falling in, the change in the field outside the BH is propagated from the additional matter that falls in.

If the BH is considered to have a singularity at it's center, all the mass is concentrated there. Actually the entire BH is that singularity, and the Event Horizon is just a boundary where the escape velocity is c.
The gravitational field would have to propagate from the center, and that poses a problem as no effects can be observed through an Event Horizon.

Edit: I don't understand how matter that is no longer there (it fell through the Event Horizon at some moment in the past) can still create a gravitational field, or cause any effects.

 

[PeterDonis]

The gravitational field would have to propagate from the center, and that poses a problem as no effects can be observed through an Event Horizon.

Why do you think this? Remember that in GR, "gravity" is not a "force" the way it is in Newtonian mechanics. Read carefully what I said about how "gravity" is modeled in GR.

Edit: I don't understand how matter that is no longer there (it fell through the Event Horizon at some moment in the past) can still create a gravitational field, or cause any effects.

Because the "field" doesn't "propagate" from the matter after it falls through the EH; it propagates from the matter while it is still collapsing, before it reaches the EH. Again, "gravity" in GR is not a Newtonian force; it doesn't "propagate" the way you are used to thinking of a force propagating. In GR, an object moves according to the curvature of spacetime right where it is, and that curvature, in so far as it "propagates" at all, propagates from events in the past light cone of where the object is. The collapsing matter, before it falls through the EH, is in the past light cone of events outside the EH for all future time, so its effects on the curvature of spacetime in that region can "propagate" just fine.

 

[Dale]

If the BH is considered to have a singularity at it's center, all the mass is concentrated there.

Not necessarily. It is only considered to be spherically symmetric. Birkhoff's theorem shows that any spherically symmetric solution of a given mass will have the same exterior metric, regardless of the details of the distribution.

 

[skeptic2]

Because the "field" doesn't "propagate" from the matter after it falls through the EH; it propagates from the matter while it is still collapsing, before it reaches the EH. Again, "gravity" in GR is not a Newtonian force; it doesn't "propagate" the way you are used to thinking of a force propagating. In GR, an object moves according to the curvature of spacetime right where it is, and that curvature, in so far as it "propagates" at all, propagates from events in the past light cone of where the object is. The collapsing matter, before it falls through the EH, is in the past light cone of events outside the EH for all future time, so its effects on the curvature of spacetime in that region can "propagate" just fine.

It sounds like you are contradicting yourself. You say, "Again, "gravity" in GR is not a Newtonian force; it doesn't "propagate" the way you are used to thinking of a force propagating." Then in the next sentence you say, "In GR, an object moves according to the curvature of spacetime right where it is, and that curvature, in so far as it "propagates" at all, propagates from events in the past light cone of where the object is." With regard to the second quote, that's exactly how I do think about forces propagating. I think we all understand that gravity is a curvature in spacetime so you can dispense with the quotation marks. It is common terminology to discuss gravitational fields without quotation marks. Though gravity may not be a force in the same context as the electric or magnetic force, changes in a gravitational field propagate much the same as changes in an electric or magnetic fields.

Are you saying the change in the curvature of spacetime of the past light cone of infalling matter remains frozen at the EH even as the matter itself passes through?

 

[PeterDonis]

Though gravity may not be a force in the same context as the electric or magnetic force, changes in a gravitational field propagate much the same as changes in an electric or magnetic fields.

Yes, no problem here.

Are you saying the change in the curvature of spacetime of the past light cone of infalling matter remains frozen at the EH even as the matter itself passes through?

Remember that I said, the curvature of spacetime at a particular event is determined by what is in the past light cone *at that event*. It's not the past light cone of the infalling matter that we're talking about; it's the past light cone of you, the observer, at some event outside the EH, after the infalling matter has collapsed through the EH. Included in your past light cone is the infalling matter *before* it passed through the EH; the effect of that infalling matter, while it was still outside the EH, is felt by you as spacetime curvature. One way of putting it is that the infalling matter leaves an "imprint" on the spacetime outside the EH as it passes, and that imprint remains after the matter has fallen through the EH.

 

[yoron]

It's a interesting question. Can something, classically 'not there', propagate?

What makes something fall into a Event Horizon is 'gravity'. Assuming that gravity is what defines 'space', what would a Black Hole be to it. Something 'not there', or something 'there'?

When we speak about a Event Horizon we are referring to a place wherefrom no radiation, or mass, can escape, that's what defines the 'information loss' from that Black Hole. Does that mean that SpaceTime doesn't notice its existence?

If I think of space as some sort of geometry it seems to me that in this geometry there are places where 'relations' are forbidden, but only at a conceptual plane, assuming now that a free falling observer indeed will pass any definition of a event horizon. We define SpaceTime from the relations we see develop under our arrow of time, and assuming that a Black Hole can 'grow' it seems to me that the Black Hole should follow the arrow we see outside it.

So a Black Hole should have a same type of arrow that we have, it also belong to the SpaceTime geometry we are in, no matter if it is 'closed' to a observer outside the event horizon. I don't expect 'space' to 'move' as we expect a wave to move myself, but I can accept the idea of it 'distorting or deforming' relative what we defined as its shape the moment before.
=

Ignoring Hawking radiation for this, also defining it as if a free falling observer can observe the whole way down it's not 'closed' to us, in reality it seems more of a one way passage.

 

[DaveC426913]

...if a free falling observer can observe the whole way down it's not 'closed' to us, in reality it seems more of a one way passage.

What's the difference?

Forgive the sloppy analogy but ... Death is a one-way passage as well. Consciousness might (if you think fancifully) live on, but since it's a one-way passage, it's forever closed to us.

 

[yoron]

Yeah, you sure got a point there, but as death is terribly controversial subject, depending on ones faith and beliefs :) I will avoid that one, or this thread might become ... But if I look at the definition of something closed to me, I shouldn't expect myself to be able to get in. It's a conceptual 'closeness' in that we all can get inside that Event Horizon, assumingly, although none of us can get back out to report what it was like.

 

[DaveC426913]

Yeah, you sure got a point there, but as death is terribly controversial subject, depending on ones faith and beliefs :)

Agreed. But it's not controversial here since atheists and believers alike are all in the exact same boat. None of us alive can know - something we all must agree on.

And controversy-wise it's analogous to "Believers in FTL travel" (to escape your black hole to report their findings) versus "FTL atheists".

 

[yoron]

heh :)