Black Holes: Draining Empty Spacetime?

[Islam Hassan]

If a black hole that is feeding is actually ingesting the spacetime around it (and hence whatever may lie in that spacetime including light) what does it do when it is not ingesting but nonetheless has very strong gravitational attraction?

Does it sit there dragging empty spacetime into it? If yes, what would be the (very very) long-term effect of this phenomenon on the evolution of the universe?


IH

 

[Orodruin]

If a black hole that is feeding is actually ingesting the spacetime around it (and hence whatever may lie in that spacetime including light) what does it do when it is not ingesting but nonetheless has very strong gravitational attraction?

This has no physical meaning and it is therefore impossible to answer your question. It is simply not a good way of describing things.

What do you think that "spacetime" is? Have you had any formal formation in special or general relativity?

 

[Islam Hassan]

This has no physical meaning and it is therefore impossible to answer your question. It is simply not a good way of describing things.

This is how I understood that fact that light cannot escape a BH, because the spacetime within which the light is traveling is itself being dragged into the BH taking the photons along with it. I may of course have understood wrong, internet science videos and resources are not necessarily accurate...


IH

 

[Orodruin]

This is how I understood that fact that light cannot escape a BH, because the spacetime within which the light is traveling is itself being dragged into the BH taking the photons along with it. I may of course have understood wrong, internet science videos and resources are not necessarily accurate...

Unfortunately, you cannot learn actual physics from watching popular science on the internet, something that has been noted countless times in this forum. Popular science is not a priori made for the audience to understand what is going on, but more to shock and awe and to have a "wow" factor to it and to create an illusion of understanding. Furthermore, you should also be very careful with video sources, in particular on the internet. There is a lot of flat out wrong things out there. Without knowing exactly what you have seen, it is impossible to say whether it is the material itself or your understanding of it (or, more likely, your understanding of it because of the previously mentioned problems with popular science) that is lacking.

Spacetime is not a substance that exists in space, it is the combination of both space and time into a (quite weird) geometric construct, where the geometry is dynamically connected to its matter and energy content. It is the geometry of spacetime and light's relation to it (only being able to follow curves with a particular property) that determines how it propagates.

 

[Ibix]

This is how I understood that fact that light cannot escape a BH, because the spacetime within which the light is traveling is itself being dragged into the BH taking the photons along with it. I may of course have understood wrong, internet science videos and resources are not necessarily accurate...

I believe that's called the "river" model. It gives an intuitive idea of how you can have things like the event horizon that is (in some senses) not moving and (in other senses) moving outward at the speed of light - like a boat moving upstream at the same speed the water moves downstream. But it's not a particularly good model for much else, so far as I understand. Honestly, I don't think it's even a really good model for the event horizon.

Basically you can't escape from a black hole because all future-directed paths curve inwards once you've crossed the horizon. There is no "flow" of spacetime inwards. Matter flows inwards, but spacetime just is.

 

[kimbyd]

I believe that's called the "river" model. It gives an intuitive idea of how you can have things like the event horizon that is (in some senses) not moving and (in other senses) moving outward at the speed of light - like a boat moving upstream at the same speed the water moves downstream. But it's not a particularly good model for much else, so far as I understand. Honestly, I don't think it's even a really good model for the event horizon.

Basically you can't escape from a black hole because all future-directed paths curve inwards once you've crossed the horizon. There is no "flow" of spacetime inwards. Matter flows inwards, but spacetime just is.

It's probably not all that terrible of an analogy, given that you can create sound horizons in fluids by forcing them to flow faster than the speed of sound in the fluid. Those sound horizons emit Hawking radiation (in the form of sound waves) just like a black hole does.

Still, best to recognize that it is still an analogy, not a description of anything that's actually happening.

 

[Stuck In a Loop]

From what I understand there is no such thing as a dormant black hole? Since it is constantly emitting radiation? Or would that just count for the event horizon?

 

[PeterDonis]

From what I understand there is no such thing as a dormant black hole? Since it is constantly emitting radiation?

Black holes theoretically should emit Hawking radiation, but any actual black hole we can see evidence for is much too large to emit any detectable Hawking radiation.

The term "dormant black hole", as I understand it, is one with no detectable accretion disk, i.e., no detectable matter is currently falling into it. Matter falling into black holes can certainly emit radiation, but only when it's falling in; if there is a period when there is no matter in the region of space near the hole, no radiation will be visible and the hole is said to be dormant.

 

[Nugatory]

From what I understand there is no such thing as a dormant black hole? Since it is constantly emitting radiation?

They aren't constantly emitting radiation, and won't for a very long time to come. The Hawking radiation from a stellar-mass block hole is like the radiant heat from an object whose temperature is just a few nanokelvins above absolute zero. The cosmic background radiation is at a temperature of a few kelvins above absolute zero, so black holes are colder than the space around them - they are net absorbers, not emitters. Only after the universe has expanded and cooled until it is colder than the black holes will they be emitters.

Matter falling into a black hole can emit enormous amounts of energy as it is heated and compressed before it reaches the horizon, but that's not coming from the black hole itself.

 

[kimbyd]

Matter falling into a black hole can emit enormous amounts of energy as it is heated and compressed before it reaches the horizon, but that's not coming from the black hole itself.

Nit: much of the energy emitted is drawn from the rotational energy of the black hole via the Penrose process.

 

[Islam Hassan]

Unfortunately, you cannot learn actual physics from watching popular science on the internet, something that has been noted countless times in this forum. Popular science is not a priori made for the audience to understand what is going on, but more to shock and awe and to have a "wow" factor to it and to create an illusion of understanding. Furthermore, you should also be very careful with video sources, in particular on the internet. There is a lot of flat out wrong things out there. Without knowing exactly what you have seen, it is impossible to say whether it is the material itself or your understanding of it (or, more likely, your understanding of it because of the previously mentioned problems with popular science) that is lacking.

Spacetime is not a substance that exists in space, it is the combination of both space and time into a (quite weird) geometric construct, where the geometry is dynamically connected to its matter and energy content. It is the geometry of spacetime and light's relation to it (only being able to follow curves with a particular property) that determines how it propagates.

Acknowledged, and indeed this is not the first time I have had this comment on PhysicsForums.

I like to download pdf and ppt slides from academic authors on select topics, public/academic lectures or courses but they are very often beyond my level of understanding and do not provide a textbook approach to things. What would be ideal really is an internet resource which is neither too simplistic in explanations of physics, too high-mathematical and is not misguided or downright misleading.

Would anyone know of such a resource?


IH

 

[Ibix]

It's probably not all that terrible of an analogy, given that you can create sound horizons in fluids by forcing them to flow faster than the speed of sound in the fluid. Those sound horizons emit Hawking radiation (in the form of sound waves) just like a black hole does.

Fair enough. I hadn't seen the analogy expressed in such precise terms, I must admit.

Still, best to recognize that it is still an analogy, not a description of anything that's actually happening.

In particular, it's going to require an energy source to keep the fluid flowing, and some kind of circulation system or source and sink to supply the fluid, neither of which is a feature of black hole horizons. I also find it difficult to imagine that it can provide a spherically symmetric horizon, or even a circularly symmetric one unless the fluid is very compressible.

 

[Orodruin]

Acknowledged, and indeed this is not the first time I have had this comment on PhysicsForums.

I like to download pdf and ppt slides from academic authors on select topics, public/academic lectures or courses but they are very often beyond my level of understanding and do not provide a textbook approach to things. What would be ideal really is an internet resource which is neither too simplistic in explanations of physics, too high-mathematical and is not misguided or downright misleading.

Would anyone know of such a resource?


IH

If you really want to understand what is going on, you cannot start from the physics side only. You need to develop the necessary mathematical knowledge at the same time. You mentioned ”textbook approach” and that is where you really should be looking (not necessarily textbooks, but teaching resources in both physics and mathematics). Of course you can look for more or less rigorous popularisations, but in the end they will never be the real deal and you will just learn in terms of analogies, which can never really be used to extrapolate to new situations.

 

[Ibix]

Would anyone know of such a resource?

I'd be rather surprised. If there were simpler ways of handling GR, scientists wouldn't bother with the complicated ways... There are specific ways of handling specific cases, of course. I think you can develop an intuitive model of special relativity, enough to handle the twin paradox, ladder and barn, and Einstein's train, from learning a few facts about Minkowski diagrams. But this can only carry you so far - you can't produce a sensible reference frame for the traveling twin this way, for example. Let alone move on to curved spacetime.

 

[m4r35n357]

I believe that's called the "river" model. It gives an intuitive idea of how you can have things like the event horizon that is (in some senses) not moving and (in other senses) moving outward at the speed of light - like a boat moving upstream at the same speed the water moves downstream. But it's not a particularly good model for much else, so far as I understand. Honestly, I don't think it's even a really good model for the event horizon.

I've decided to try sticking my neck out here, and say that as far as I have learned the river model does represent motion of a non-static spacetime.

I would refer to the first few equations here. If you apply the simple diagonal equation for speed of light to Schwarzschild coordinates you get something like:

$\frac {dr} {dt} = \frac{2M} {r} - 1$

so if the radial light speed is 0 at the horizon, where of course c = 1 ;) this IMO describes light moving at c against an inflow of spacetime at$\frac{2M} {r}$, and the river model formalizes this idea in terms of Gullstrand-Painleve coordinates.

So, do I need an attitude adjustment? ;)

 

[Nugatory]

and the river model formalizes this idea in terms of Gullstrand-Painleve coordinates.

I think it's the other way around: Whatever the model is, GP coordinates formalize it.

As for whether light is moving at $c$ against an inflow of spacetime, or whether light is moving at c relative to an arbitrarily chosen point that is itself not at rest... That's two different informally stated models, both of which are formalized by GP coordinates. Either model may be helpful in visualizing any particular problem, both should be ignored unless they're helping visualize the coordinates.

 

[PeterDonis]

as far as I have learned the river model does represent motion of a non-static spacetime.

Only one problem: Schwarzschild spacetime outside the event horizon is static.

If you apply the simple diagonal equation for speed of light to Schwarzschild coordinates

Those are the wrong coordinates if you're interested in the river model; that model is specifically based on Painleve coordinates.

if the radial light speed is 0 at the horizon

It isn't for all light in Painleve coordinates. See below.

the river model formalizes this idea in terms of Gullstrand-Painleve coordinates

Yes, which means that, as above, you can't use equations from Schwarzschild coordinates in this context. In Painleve coordinates, the coordinate speed of light moving radially is

$$
\frac{dr}{dT} = - \sqrt{\frac{2M}{r}} \pm 1
$$

where the $+$ sign is for outgoing light and the $-$ sign is for ingoing light. So radially outgoing light at the horizon has a coordinate speed of zero, but radially ingoing light does not. (In Schwarzschild coordinates, the coordinate speed of light is the same for outgoing and ingoing.)

 

[m4r35n357]

Only one problem: Schwarzschild spacetime outside the event horizon is static.

Ack. My weasel words using both coordinates were due to an error in my Maxima sheet (seemingly introduced since I last used it!) . . . . now fixed.
Thanks!

 

[kimbyd]

I also find it difficult to imagine that it can provide a spherically symmetric horizon, or even a circularly symmetric one unless the fluid is very compressible.

No, it's definitely not spherically-symmetric!

What's done is to move the fluid at very high speed through a narrowing pipe. As the pipe narrows, the fluid is forced to increase its speed. At the position where the speed of the fluid through the pipe becomes faster than the speed of sound within the fluid, a sound horizon forms.