Black holes

[Ziggurat]

In what context are you looking for the definition of black then?

Black holes and black bodies. It's the same definition in both cases, and I already gave you the definition in my previous post.

 

[Zeuzzz]

In no context does "black" mean some frequency of the EM spectrum responsible for visible light. Even as a possible misunderstanding caused by a term from one context misapplied to another, it makes no sense.

Meant wavelength, stupid mistake.

I seem to remember something about color being due to molecules different electron transitions between energy states, which thus release photons of varying frequency/color, and the combination of this and how the molecule interacts with the EM spectrum is how color is physically defined.


So a black object presumably absorbs all of the visible EM spectrum.

 

[Vorpal]

There's a straightforward correspondence between wavelength and frequency. The issue is that what you just described is a physical basis of 'color' as in chrominance, but not luminance, i.e., brightness. In colloquial use, 'black' is commonly understood as as lack of brightness, so if your notion of 'color' refers to chrominance only, it would follow that 'black' is not a color in the first place.

But if you generalize your last definition as absorbing all of the EM spectrum, not just visible, of the radiation incident on it, then it's exactly the sense of "black" in "black body". But then under this definition, that says nothing about how bright the object is at all.

The meaning of words is context-dependent. Surprise.

 

[Reality Check]

The Schwarzschild mathematics tells you something important, and when you disregard it you end up with a non-real solution.

This is where you reamin wrong - no one is ignoring Schwarzschild coordinates ("mathematics ").
What is happening is that you are ignoring all of the other coordinate systems.

When you ignore all coordinate systems as GR does then you get the real situation where external observers measure time dilation as a clock approaches the event horizon while an observer with the clock measures no time dilation.

If you use a specific coordinate system then you get the results specific to that coordinate system where there may or may not be a singularity at the event horizon. That is why that is called a coordinate singularity. It is not real - it is an artifect of the coordinate system.

One more time:
Alice decides to use Schwarzschild coordinates and she measures that there is a singularity at the event horizon.
Bob decides to use Kruskal–Szekeres coordinates and he measures that nothing special happens at the event horizon.

 

[Brian-M]

So a black object presumably absorbs all of the visible EM spectrum.

Exactly. And ideal black-bodies absorb the entire EM spectrum.

Interestingly, objects emit the same frequencies of the EM spectrum that they absorb, so a perfect black-body should be able to emit all the frequencies in the EM spectrum.

Although, the higher the frequency the hotter they have to be to emit measurable quantities of photons in that specific wavelength. Think about how steel glows red when very hot, but glows yellow and white when even hotter. That's because when it's glowing red-hot, it's still not hot enough to emit noticeable amounts of yellow or blue light.

This is basically what thermal radiation is, even a room-temperature object or a block of ice will emit photons, but just at levels and frequencies too low to detect without special equipment.

I think I remember reading something about Hawking radiation being the black-hole equivalent to thermal radiation. Can anyone here tell me if this is in any way true? (I know, completely different process. But is it equivalent/analogous to regular thermal radiation?)

 

[Ziggurat]

I think I remember reading something about Hawking radiation being the black-hole equivalent to thermal radiation. Can anyone here tell me if this is in any way true? (I know, completely different process. But is it equivalent/analogous to regular thermal radiation?)

The details of the emission are different, but the result is the same: it's a blackbody spectrum. Black holes have a temperature that's related to their size. The smaller they are, the hotter they are. A stellar mass-sized black hole will be quite cold, but a micro-black hole (the sort that some people think particle accelerators might produce) would be exceedingly hot, and would radiate its mass energy away too quickly to ever grow.

 

[Octavo]

Apologies if this is a grossly stupid question (or has already been answered), but assuming you cross the event horizon of a black hole large enough that you survive this process unscathed: looking toward the singularity would you see anything?

Assume for a second the singularity is emitting photons (like a star, still fusing stuff and radiating light), would you suddenly see a star pop into life in front of you as you cross the event horizon?

Do singularity's radiate anything? I know nothing could escape the event horizon, but theoretically, could the <whatever process happens in the singularity as matter is sucked in> create new <exotic particles> that are radiated away from the singularity (however briefly)?

 

[W.D.Clinger]

Farsight's argument is founded upon his misinterpretation of the Schwarzschild mathematics:

The Schwarzschild mathematics tells you something important, and when you disregard it you end up with a non-real solution.

Although Farsight's argument is essentially mathematical, he gets upset when someone uses genuine mathematics to explain what's wrong with Farsight's argument:

All: as ever Clinger has no argument, does not respond to the issue I raised, and tries to bury the discussion with mathematics that most readers don't follow. Don't buy it. It's smoke and mirrors, it's Emperor's New Clothes. Insist on scientific evidence and factual English. If somebody offers a mathematical expression to support this, fair enough, but demand a list of terms. If somebody gives you a complex expression without a list of terms, be sceptical. They may be trying to pull the wool over your eyes.

Anyone who can follow basic differential calculus and algebra can follow the exercises I posted. Because this is the Science, Mathematics, Medicine, and Technology subforum, most of this subforum's readers can work through the exercises for themselves (apart from exercise 8). Several readers have already done that.

If Farsight (or anyone else) needs help with those exercises, all they have to do is ask. The exercises are most valuable to those who work through them on their own, but I'd be happy to post a solution for any exercise that's giving you trouble.

I started by listing the basic definitions. If anyone wants me to define any of the mathematical or scientific terms I've used, all they have to do is ask.

Don't pick a coordinate system!

Had Farsight followed that advice, he wouldn't have picked the Schwarzschild coordinate system as the basis for his entire argument.

What I won't do is roll over when somebody like Clinger tries to pull the you don't understand the maths trick.

If Farsight can't defend his mathematics, then he shouldn't be using Schwarzschild coordinates as the basis for his argument.

If Farsight can't defend his mathematics, then he shouldn't be telling us he's the only one here who understands the math.

If Farsight can't defend his mathematics (and he can't), then he shouldn't be writing stuff like this:

I don't think you're moronic, ben. I think you're hubristic and dishonest.

 

[Brian-M]

Apologies if this is a grossly stupid question (or has already been answered), but assuming you cross the event horizon of a black hole large enough that you survive this process unscathed: looking toward the singularity would you see anything?

Assume for a second the singularity is emitting photons (like a star, still fusing stuff and radiating light), would you suddenly see a star pop into life in front of you as you cross the event horizon?

Do singularity's radiate anything? I know nothing could escape the event horizon, but theoretically, could the <whatever process happens in the singularity as matter is sucked in> create new <exotic particles> that are radiated away from the singularity (however briefly)?

Just a quick guess (I could be wrong)... but once you cross the event horizon every point between you and the singularity will have an escape velocity greater than the speed of light. Effectively, you'd have infinite event horizons between you and the singularity. So from your point of view, it'd be no different than if you were looking into the black hole from just outside the event horizon.

 

[ctamblyn]

Apologies if this is a grossly stupid question (or has already been answered), but assuming you cross the event horizon of a black hole large enough that you survive this process unscathed: looking toward the singularity would you see anything?

Assume for a second the singularity is emitting photons (like a star, still fusing stuff and radiating light), would you suddenly see a star pop into life in front of you as you cross the event horizon?

Do singularity's radiate anything? I know nothing could escape the event horizon, but theoretically, could the <whatever process happens in the singularity as matter is sucked in> create new <exotic particles> that are radiated away from the singularity (however briefly)?

On another thread a few days back, I posted the following link:

http://jila.colorado.edu/~ajsh/insidebh/schw.html

They have some simulated videos of what it would look like to fall into various kinds of black hole.

 

[Roboramma]

Just a quick guess (I could be wrong)... but once you cross the event horizon every point between you and the singularity will have an escape velocity greater than the speed of light. Effectively, you'd have infinite event horizons between you and the singularity. So from your point of view, it'd be no different than if you were looking into the black hole from just outside the event horizon.

It's also cool to think of in light of what Ziggurat posted:

Once you're inside, there is no direction to the singularity. The singularity is everywhere. But it's everywhere in the future. You don't need to move to get to the singularity, you just need to wait. Motion only changes how long the wait is.

And I think we all understand that you can't see the future.

 

[Octavo]

Just a quick guess (I could be wrong)... but once you cross the event horizon every point between you and the singularity will have an escape velocity greater than the speed of light. Effectively, you'd have infinite event horizons between you and the singularity. So from your point of view, it'd be no different than if you were looking into the black hole from just outside the event horizon.

Ahhh... yes of course, that makes sense. Pretty boring though. One would have hoped that if you were travelling into a black hole, the least it could do is give you a decent show

 

[sol invictus]

Ahhh... yes of course, that makes sense. Pretty boring though. One would have hoped that if you were travelling into a black hole, the least it could do is give you a decent show

You'll certainly see some interesting things as you're getting spaghettified by the singularity, but I'm not sure how much attention you could pay to them.

But yes, as others have said, black hole singularities are to the future - they are much like a cosmological big crunch.

 

[Ziggurat]

Ahhh... yes of course, that makes sense. Pretty boring though. One would have hoped that if you were travelling into a black hole, the least it could do is give you a decent show

Well, if you fell into a black hole that collapsed from a neutron star, then (at least in principle) you would be able to see the surface of the neutron star as it continued to collapse towards the singularity. You would hit the singularity yourself before you saw the star collapse into a singularity, and in practice everything might be too red-shifted to really see much of anything, but the possibility is still there to watch as it continued collapse inside the event horizon.

 

[Reality Check]

RC: Hawking is a celebrity physicist, a "high priest" whose medical condition insulates him from media criticism, and whose actual contribution to physics is scant. Don't think his word is gospel. We should start a thread on Hawking radiation some time.

Farsight, Hawking's word is not gospel and I have never treated it as gospel. I know that he has been wrong at least once (black holes & information)
I stated that black holes are black (any light emitted within the event horizon cannot escape from the event horizon).

There is little to discuss anout Hawking radiation.

Don't pick a coordinate system!

Farsight, Don't pick a coordinate system!
Do not obsess on Schwarzschild coordinate system (where there is a singularity at the event horizon).

Instead look at the fact that this singularity only exists beecause you have picked this coordinate system and does not exist in other coordinate system. So if we have 2 observers looking at a clock falling into a black hole:
Alice decides to use Schwarzschild coordinates and she measures that there is a singularity at the event horizon.
Bob decides to use Kruskal–Szekeres coordinates and he measures that there is no singularity at the event horizon.

 

[Thabiguy]

So. In this thread about black holes, I'd like to ask a few questions. Unlike special relativity, which is relatively straightforward and simple in comparison, general relativity has never been my strong suit when it comes to trickier stuff, and I hope someone more knowledgeable can give me a helping hand here. It is of course okay to speculate, but I would especially appreciate answers from those who are reasonably sure about what the theories predicts.

For simplicity, let's consider a simple Schwarzschild black hole, a supermassive one, so that tidal forces don't give us much trouble. We throw in a probe, and observe everything from a safe distance. (Unless specified otherwise, let all further observations be from the viewpoint of a distant observer.) The probe transmits as it approaches the horizon, reporting nothing out of the ordinary. Then its transmissions slow down and disappear. The probe is stuck there right above the event horizon, invisible, flattened and frozen in time. So far, so good.

Now, we grab a lot of matter, as much as the mass M of the black hole itself (it's a thought experiment, so let's not worry about the logistics) and throw it in as well. Yay! The black hole now has mass 2M and its horizon is considerably farther out.

My first question is: from our viewpoint, where's the probe now? I see two major possibilities: either the probe is still where it was, i.e. at a point which is now below the horizon, or it actually moved out as the black hole's horizon expanded. Which is it? (I used to assume the former, but now I think the latter looks more likely.) - If the former is true, the logical consequence would be that the singularity is at the center of the black hole, surrounded by all the matter that fell in - our probe being a sample of it - that now fills the horizon. If the latter is true, the logical consequence would be that there is nothing inside the horizon, and everything that ever fell in, including the core of the original collapsing star, is still in a thin superdense bubble just outside the horizon, and the central singularity is not below the horizon, but exactly at it (from our distant viewpoint). Is the reasoning correct?

Now, let's put Hawking radiation in the picture. We get rid of CMBR (again, it's a thought experiment, so let's not worry about the logistics) and wait a really, really long time. The black hole should slowly radiate away. Let's wait until the black hole that remains is half the original mass (M/2). The event horizon has shrunk considerably. Regardless of where the probe was in question one, now it must be closer to the center - it has passed through where the event horizon had been at the time we threw the probe in.

If during our superlong wait, we recorded everything, and then played it superfast, presumably there should be at least a little more transmission from the probe (albeit muffled by all the mass we threw in after the probe). My second question is: how much more would we hear from the probe? Would we just hear it get a little closer to the original location of the horizon at the time we threw it in, or would we actually hear it transmit about passing the original horizon location and falling further in, to where it is now? (The latter sounds more likely to me, but I'm not sure.)

By now, a lot of the mass of the black hole has radiated away, and it is no longer there. My third question: can we tell which mass has disappeared and was converted to radiation? Was it the original collapsing star and the first of the infalling matter that, from our distant viewpoint, finally reached the singularity by this time? Was it the last of the infalling matter?

A related point to consider: if we replay in fast motion our recorded observation of the black hole radiating away, we realize that the black hole is essentially a huge ongoing explosion, slowed down in time from our distant viewpoint. My fourth question: what implications does this have for our probe? We threw our probe in, and since then, we've seen a huge amount of energy hurled back at us from the black hole. All this energy has already reached us by now, so does this mean the probe must have already encountered all this energy on its way down? Wouldn't it be incinerated by this enormous amount of energy? Was it already destroyed by now and itself returned to us in the form of Hawking radiation - or is it still hovering above the horizon, frozen in time, and all the energy radiated from the black hole shrinking underneath it somehow... went around it?

Of course, it needn't be either-or; some of these questions may have answers I haven't thought of. I'll be glad to hear your thoughts.

 

[ben m]

The Schwarzschild mathematics tells you something important, and when you disregard it you end up with a non-real solution.

How can you tell? What mathematical, physical, or geometric test did you apply before making this determination?

What test do Schwarzschild coordinates pass, that Lemaitre coordinates fail?

(Is the test "Lemaitre coordinate systems fail because they don't prove me right, and I know I'm right"?)

 

[Octavo]

So. In this thread about black holes, I'd like to ask a few questions. Unlike special relativity, which is relatively straightforward and simple in comparison, general relativity has never been my strong suit when it comes to trickier stuff, and I hope someone more knowledgeable can give me a helping hand here. It is of course okay to speculate, but I would especially appreciate answers from those who are reasonably sure about what the theories predicts.

I freely admit I know next to nothing about this subject, so consider all of my following statement pure speculation pulled from my butt,

Now, let's put Hawking radiation in the picture. We get rid of CMBR (again, it's a thought experiment, so let's not worry about the logistics) and wait a really, really long time. The black hole should slowly radiate away. Let's wait until the black hole that remains is half the original mass (M/2). The event horizon has shrunk considerably. Regardless of where the probe was in question one, now it must be closer to the center - it has passed through where the event horizon had been at the time we threw the probe in.

If during our superlong wait, we recorded everything, and then played it superfast, presumably there should be at least a little more transmission from the probe (albeit muffled by all the mass we threw in after the probe). My second question is: how much more would we hear from the probe? Would we just hear it get a little closer to the original location of the horizon at the time we threw it in, or would we actually hear it transmit about passing the original horizon location and falling further in, to where it is now? (The latter sounds more likely to me, but I'm not sure.)

It would seem to me that you would hear nothing from the probe. The probe and all the information is was sending got sucked into the singularity very shortly after crossing the event horizon. Even if the event horizon shrunk to a diameter smaller than the probe itself, that information was destroyed by the singularity.

I would suppose the only way you *may* get information from the probe would be if you had some way to reconstruct that information from the hawking radiation?

 

[Thabiguy]

It would seem to me that you would hear nothing from the probe. The probe and all the information is was sending got sucked into the singularity very shortly after crossing the event horizon. Even if the event horizon shrunk to a diameter smaller than the probe itself, that information was destroyed by the singularity.

Well, even in the classical case (no Hawking radiation, black holes can only grow) we should be able to hear a little more - we could hear the probe come closer and closer to the horizon, although we would have to wait ever increasing periods of time to collect ever shorter pieces of transmissions. The question is how much more we would hear when the consequences of Hawking radiation are added in the picture.

The probe and all the information is was sending got sucked into the singularity very shortly after crossing the event horizon.

Possibly, but for an outside observer, the probe hasn't crossed the event horizon, and will never have crossed it, no matter how long we wait. For the classical case, this would be the end of the story - the portion of the probe's flight below the horizon would simply lie beyond infinitely distant future for us, the remote observers. We couldn't hear transmissions from inside as we couldn't wait longer than infinitely long. For us, nothing could get out because nothing could get in, in the first place.

But Hawking radiation screws everything up. First and foremost, as all the mass that ever fell in, including the mass of our probe, will eventually be radiated out in a long but finite amount of time (at least in our thought experiment where we got rid of CMBR), this means that whatever we perceived as the horizon, can't really have been an event horizon to begin with.

As I hinted in my earlier set of questions, I can think of a couple of plausible scenarios what we might observe if we waited long enough. One thing we seem to be able to rule out is that the probe would simply continue to hang frozen above the shrinking horizon, as in the classical case. Eventually, the mass of the black hole will be less than the mass of the probe, by which time it will be obvious that the probe can no longer be hanging there. Thus the question is what will have happened to it by then.

First seemingly consistent possibility is that almost all of the infalling matter is still hanging above the horizon at the time we throw in our probe, and if we look really well as we wait, we will see first the core of the original star and then more and more surrounding matter disappear at or near the central singularity, which for us lies exactly at the location of the apparent horizon (so we can't really see the singularity itself) and reappear as Hawking radiation, which somehow escapes through all the outer layers of infalling stuff (possibly via some quantum tunnelling?). Eventually, we will see (in super slow motion) our probe get crushed by tidal forces and fall into the singularity as well. This would imply that the probe, from its viewpoint, wouldn't encounter significant amount of Hawking radiation as it falls in. It would just see the horizon recede in front of it due to general-relativistic effects until it is destroyed by the ever-increasing gravity.

Another seemingly consistent possibility is that the probe will never fall into the singularity, but will be blasted to pieces by the Hawking radiation of all the matter that had fallen in earlier, which gets converted to energy and hurled back at the probe before it has a chance to fall in itself. This would have been made possible by the fact that the horizon is not a real event horizon (as evidenced by black hole evaporation) and so it's not really the case that all paths must inevitably lead into the singularity. This would imply that the probe, from its viewpoint as it falls, would see the black hole under it accelerate in time and its Hawking radiation increase, until the probe sees the black hole for the explosion that it really is and becomes part of the explosion, instead of reaching the singularity.

Since both can't be true, I think theory should be able to rule out at least one of these possibilities. But I can't really tell which. Perhaps some of the experts here know more. And maybe this isn't even theoretically resolved yet and nobody knows. I wonder.

 

[sol invictus]

For simplicity, let's consider a simple Schwarzschild black hole, a supermassive one, so that tidal forces don't give us much trouble. We throw in a probe, and observe everything from a safe distance. (Unless specified otherwise, let all further observations be from the viewpoint of a distant observer.) The probe transmits as it approaches the horizon, reporting nothing out of the ordinary. Then its transmissions slow down and disappear. The probe is stuck there right above the event horizon, invisible, flattened and frozen in time. So far, so good.

When you say "the probe is stuck there" you are making an implicit assumption or choice about which set of coordinates you wish to use. In some coordinates that's true, in others it's not. Think about the waterfall analogy (does the probe get "stuck" at the point where the flow velocity exceeds the speed of sound?), or the relativity of simultaneity.

Now, we grab a lot of matter, as much as the mass M of the black hole itself (it's a thought experiment, so let's not worry about the logistics) and throw it in as well. Yay! The black hole now has mass 2M and its horizon is considerably farther out.

My first question is: from our viewpoint, where's the probe now?

Ill-defined question, for the same reason as above.

At least in classical gravity there's no limit to how late you can receive a signal from the probe. In the coordinate systems that naturally describe this, you'd say the probe is inside the horizon and interpret such late signals as emitted before the probe crossed it, so they simply took a long time to escape.

But coordinates exist in which it never crosses the horizon. In those coordinates, it gets frozen at the larger (final) radius of the event horizon.

If the latter is true, the logical consequence would be that there is nothing inside the horizon, and everything that ever fell in, including the core of the original collapsing star, is still in a thin superdense bubble just outside the horizon, and the central singularity is not below the horizon, but exactly at it (from our distant viewpoint). Is the reasoning correct?

No. Those coordinates don't cover the interior in any natural way. It would be better to stop asking about where and when things are - those aren't well-defined questions - and instead ask about the results of experiments you could perform. One would be to jump into the black hole. If you do that, you don't hit the singularity right after crossing the horizon. In your growing black hole example, it would take longer to hit the singularity if you jumped in later (I'm pretty sure - I could check). But in any case, the singularity is never right below the horizon in that sense.