# Black hole formation watched from a distance

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How is black hole formation observed by a distant observer?
Dear all,

For a new book I'm writing I'm investigating some common misconceptions in physics. And of course, that means confronting myself with my own confusion. One thing I've never got clear in my head, and which I find hard to answer using google and my textbooks on GR, is the following: how exactly is black hole formation observed by an observer sitting at a distance? If we take a solution of, say, infalling matter or light, crushing itself into a black hole, how much coordinate time would an observer at a distance measure for the matter or light to form an event horizon? I'm sure this can be answered technically by looking at Penrose diagrams, but I've never felt completely comfortable with those. My intuitive answer would be that it would take a huge amount of coordinate time (an infinite amount?) according to our observer for the matter to collapse into a volume smaller than its Schwarzschild radius such that the event horizon actually forms. Am I right? And if so, can someone give some details? What would this mean concretely for the black holes we observe, especially the famous picture by the Event Horizon Telescope? In the end I want to translate this to something concrete in my book, like this picture.

As a follow up one could also ask the same question about black hole evaporation of course, but let's first focus on the black hole formation process. Any insights are more than welcome.

Greg Bernhardt and AJT

martinbn
Is there a reason why you expect that the answer shouldn't depend on what exacly the formation is, and on what time coordinate you use? Or do you have something more specific in mind?

Is there a reason why you expect that the answer shouldn't depend on what exacly the formation is, and on what time coordinate you use? Or do you have something more specific in mind?
Well, let's compare to the particle which flies into the black hole from great distance: a distant observer measures an infinite coordinate time between the events "particle starts traveling" and "particle enters horizon", while the particle itself measures a finite proper time between the same two events. But when it comes to the observation of the actual formation of the black hole, I have intuitive doubts (I know, nature doesn't care about my intuition).

Does the event horizon form in a finite amount of coordinate time according to the distant observer? I.e., when we see the famous Event Horizon picture of the black hole, is it plausible that the formation of the black hole and its event horizon is in a much more advanced stadium than from our perspective?

jbriggs444
Homework Helper
Does the event horizon form in a finite amount of coordinate time according to the distant observer?
Unlike the situation in the flat space-time of special relativity, specifying an observer is not enough to specify a global coordinate system.

If you want Schwarzschild coordinates, you have to say so.

Unlike the situation in the flat space-time of special relativity, specifying an observer is not enough to specify a global coordinate system.

If you want Schwarzschild coordinates, you have to say so.
Yes, let's take Schwarzschild coordinates, and put Earth at r= far away from the black hole (at r=0; horizon at r=2M).

vanhees71
martinbn
What are Schwarzshild coordinates?

vanhees71
Gold Member
martinbn
Is this for my question? The thread is about black hole formation. The Schwarzschild is eternal it cannot be relevant.

PAllen
Well, the standard simple model of gravitations collapse to BH, rather than eternal case, is the Oppenheimer-Snyder solution. The following notes cover this collapse in a modern way, then discusses trapped surfaces and light escape during the process (also, generalizing to fluid ball rather than dust ball):

http://events.asiaa.sinica.edu.tw/school/20070129/talk/960201rezzolla.pdf

In any case, as to what you would visually 'see' from a distance during and idealized collapse (i.e. no remaining accretion disc), this was well covered way back circa 1970 in MTW - within a quite short amount of proper time for the distant observer, the collapsing star would be blacker than empty intergalactic space. Thus, the term black hole was coined. The light that will emanate forever from the near outside of the horizon is of such low frequency and intensity that it could never be observed in principle (imagine a detector for 'photons' with wavelength of 1 light year arriving once per month).

SolarisOne, CalcNerd, haushofer and 1 other person
PAllen
Well, the standard simple model of gravitations collapse to BH, rather than eternal case, is the Oppenheimer-Snyder solution. The following notes cover this collapse in a modern way, then discusses trapped surfaces and light escape during the process (also, generalizing to fluid ball rather than dust ball):

http://events.asiaa.sinica.edu.tw/school/20070129/talk/960201rezzolla.pdf

In any case, as to what you would visually 'see' from a distance during and idealized collapse (i.e. no remaining accretion disc), this was well covered way back circa 1970 in MTW - within a quite short amount of proper time for the distant observer, the collapsing star would be blacker than empty intergalactic space. Thus, the term black hole was coined. The light that will emanate forever from the near outside of the horizon is of such low frequency and intensity that it could never be observed in principle (imagine a detector for 'photons' with wavelength of 1 light year arriving once per month).
Actually, adding some detail from MTW, when the quantum nature of emission is considered, about 10 milliseconds (of distant observers proper time) after a distant observer sees a collapsing 10 solar mass star begin to dim, the last photon they will ever see arrives. Note that Hawking radiation does not change this because for more that a 100 billion years, the BH is growing by absorbing CMB radiation, rather than shrinking by emitting Hawking radiation. The relevant discussion is pp. 872-3 of MTW.

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CalcNerd and vanhees71
PAllen
Actually, adding some detail from MTW, when the quantum nature of emission is considered, about 10 milliseconds after a distant observer sees a collapsing 10 solar mass star begin to dim, the last photon they will ever see arrives. Note that Hawking radiation does not change this because for more that a 100 billion years, the BH is growing by absorbing CMB radiation, rather than shrinking by emitting Hawking radiation. The relevant discussion is pp. 872-3 of MTW.
Note, it also follows, that a visible EH in the sense of the EH telescope forms within 10 milliseconds of the beginning of catastrophic collapse for a 10 solar mass star. Note, this is consistent with the time scales of BH merger events, where two BH of masses of 10s of solar masses merge within 2 seconds or less, once they get close, emitting 3 solar masses of energy as GW in much less than a second - all as observed from earth. The same fallacious 'takes forever' arguments would apply to BH mergers, except, of course, that they are fallacious.

haushofer and vanhees71
Well, you could go back to the original paper on the matter, "On continued gravitational contraction" by Snyder and Oppenheimer.

Which, I only know because of this lecture by Jacobson:

vanhees71
PAllen
Well, you could go back to the original paper on the matter, "On continued gravitational contraction" by Snyder and Oppenheimer.

Which, I only know because of this lecture by Jacobson:

Well, I am familiar with this paper, and could have linked to it. However, it has some issues for the purpose at hand, and from the modern point of view. It stops its analysis when the dust boundary reaches the horizon, noting that this happens in finite proper time for a boundary riding observer, but infinite coordinate time for a distant observer per the chosen coordinates. It does not examine at all what happen to the dust after horizon crossing. The paper I linked follows the dust all the way to the singularity, and distinguishes coordinate features from observations. Further, it generalized to the more plausible fluid case, noting differences in the formation of apparent and true horizons in this case. Thus, I made a deliberate, IMO, well founded, decision not to link this paper.

Does anyone insist on linking to Maxwell's original papers when discussing electromagnetism?

vanhees71 and romsofia
Well, I am familiar with this paper, and could have linked to it. However, it has some issues for the purpose at hand, and from the modern point of view. It stops its analysis when the dust boundary reaches the horizon, noting that this happens in finite proper time for a boundary riding observer, but infinite coordinate time for a distant observer per the chosen coordinates. It does not examine at all what happen to the dust after horizon crossing. The paper I linked follows the dust all the way to the singularity, and distinguishes coordinate features from observations. Further, it generalized to the more plausible fluid case, noting differences in the formation of apparent and true horizons in this case. Thus, I made a deliberate, IMO, well founded, decision not to link this paper.

Does anyone insist on linking to Maxwell's original papers when discussing electromagnetism?
OP is writing a book, and I personally like books that talk about the history of the subject, while also discussing the physics, and subsequent progression. If this were just a post about the topic, your link would suffice since it's modern AND through.

However, the lecture notes you posted don't mention the original work, and I would be remiss if I didn't mention it given the context (and my bias for books :-) )

vanhees71
PAllen
OP is writing a book, and I personally like books that talk about the history of the subject, while also discussing the physics, and subsequent progression. If this were just a post about the topic, your link would suffice since it's modern AND through.

However, the lecture notes you posted don't mention the original work, and I would be remiss if I didn't mention it given the context (and my bias for books :-) )
Yes, definitely agreed. I hadn’t thought of that aspect. Here is the Oppenheimer Snyder original:

https://journals.aps.org/pr/pdf/10.1103/PhysRev.56.455

vanhees71
vanhees71
Gold Member
Is this for my question? The thread is about black hole formation. The Schwarzschild is eternal it cannot be relevant.

martinbn
But it doesn't, because my question was "what are Schwarzschild coordinates for a black hole?", not just for the Schwarzschild black hole.

vanhees71
Gold Member
I thought Schwarzschild coordinates refer to the Schwarzschild solution and thus also a Schwarzschild black hole. For other black holes (most usefully FAPP Kerr black holes) of course you use other coordinates.

PeroK
Homework Helper
Gold Member
2020 Award
But it doesn't, because my question was "what are Schwarzschild coordinates for a black hole?", not just for the Schwarzschild black hole.
Do you mean the time-dependence of the star collapsing to within its previous surface? You have a dynamic collapsing solution between a static initial solution an approximately static end solution?

martinbn
Do you mean the time-dependence of the star collapsing to within its previous surface? You have a dynamic collapsing solution between a static initial solution an approximately static end solution?
I meant that I understand the question to be about a generic formation of a black hole.

PeroK
Homework Helper
Gold Member
2020 Award
I meant that I understand the question to be about a generic formation of a black hole.
That leaves me none the wiser regarding your question, I'm sorry to say.

pervect
Staff Emeritus
You might want to consider what case you want to understand, and what you want to observe. A couple of possible things I can think of observing - "hot" test particles emitting a known proper frequency, and of course gravitational waves.

What case you want to study is also important. The simple cases are unfortunately probably not representative of what actually happens. The issue as I understand it is stability. Perfect spherical symmetry is a natural assumption to make, but since it is felt that actual solutions diverge in an unstable manner from the perfectly symmetrical case, the perfectly spherical case is probably misleading. Unfortunately, the realistic non-spherical cases are hard.

Openheimer-Snyder solutions, which were previously mentioned, would represent the unstable perfectly spherical collapse.

This is a bit generic, so lets give something more specific. Consider what's called "mass inflation", and it's impact on the stability of horizons. Poisson and Israel have some papers on mass inflation, IIRC. Google finds https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.63.1663

Gravitational wave emission from binary inspirals have been extensively studied, though they require numerical simulations. I've read bits and pieces about these simulations, but I don't recall any of the details or authors. It isn't something I consdier that I really understand, and is something I'd like to understand much better than I do. Probably digging into the Ligo papers would give a starting place, at least.

There are some other papers on realistic, rotating, and non-spherical collapse, but from what I recall reading it's dificult and not fully understood. It may have been Andrew Hamilton that wrote some of what I read, but I don't really recall for sure.

PAllen
The OP asked mostly for, IMO, for qualitative statements about observation of BH formation by a distant observer. For this, I think the description in MTW and the lecture notes I provided is sufficient. However the author of the lecture notes I linked is an expert in numerical relativity analyses of realistic collapse. The following are two professional papers by this author on realistic collapse. Unfortunately, they don’t have much to say on the observations of distant observers:

https://arxiv.org/abs/gr-qc/0403029
https://arxiv.org/abs/gr-qc/0503016

Note, it also follows, that a visible EH in the sense of the EH telescope forms within 10 milliseconds of the beginning of catastrophic collapse for a 10 solar mass star. Note, this is consistent with the time scales of BH merger events, where two BH of masses of 10s of solar masses merge within 2 seconds or less, once they get close, emitting 3 solar masses of energy as GW in much less than a second - all as observed from earth. The same fallacious 'takes forever' arguments would apply to BH mergers, except, of course, that they are fallacious.
Thanks! I took a quick glance at MTW, which I only have as a pdf, so I hadn't thought about consulting it. I also wasn't really familiar with the explicit Oppenheimer-Snyder solution, so I'll definitely take a look at that. Just to be sure: can we state that for us on earth the formation of a black hole would take an infinite amount of time if we define "formation of the black hole" by "the star has shrunk to its gravitational radius" (as Oppenheimer and Snyder), but that the difference between this asymptotic state (as observed by us from earth) and the black hole as observed by a "cocollapsing observer" is for all practical purposes zero within a very small timescale?

I'll dive into the other reactions too, but due to a fusion at school things are a bit hectic. Do know that I read and appreciate every reaction!

By the way, it's historically quite curious that the Oppenheimer-Snyder paper was written when Europe was collapsed into World War 2. I'm sure this has been poetically expressed by other authors before ;)

PAllen