How does the event horizon of a Schwarzchild black hole nucleate and develop?

[oldman]

I would be grateful if someone could point me to a description of how a sphere of freely infalling matter ---- say equivalent to that of a collapsing massive star --- generates an finite-sized event horizon, as observed far from the incipient black hole.

I can only imagine that the event horizon nucleates at a point near the sphere's centre, where infall creates the densest matter, and "then" dilate as it gobbles up more matter. But I get confused about how an external observer would "see" this black horizon nucleate and grow: for such an observer any event horizon must be eternally frozen in time.

Then I tell myself that the horizon is after all only a coordinate singularity, not a physical object, and that it could (in principle, somehow) be observed over a finite time as a black dilating sphere that propagates outward through the infalling matter until all has been consumed and an appropriate sized black hole has developed.

Otherwise how would finite-sized black holes ever come to "exist" for external observers, such as ourselves studying our galaxy centre?

A possible 1-dimensional analogy would be behaviour of speeding nose-to-tail freeway traffic when someone momentarily brakes. This can cause a density wave of cars (analagous to the event horizon) to propagate backward ---- just a traffic pattern rather than a physical entity (although the wave amplitude can rise and cause multiple crashes!).

If my fevered imagining is anywhere correct, do black holes nucleate as point singularities? If so, are the tidal forces during nucleation not extreme? at an event horizon they increase as the mass of the hole gets smaller.

 

[George Jones]

Because the event horizon is a null hypersurface, an external observer can never see it, just like an event on a lightcone in Minkowski spacetime can never be seen by observers outside the lightcone. Yes, the tidal forces at the event horizon start off at infinity (horizon and physical singularity together) and progressively diminish as the star is swallowed. For a Penrose diagram of black hole formation from spherical stellar collapse, see page 199 (pdf page 206) of the on-line version of Sean Carroll's book,

http://xxx.lanl.gov/abs/gr-qc/9712019.

 

[oldman]

...For a Penrose diagram of black hole formation from spherical stellar collapse, see page 199 (pdf page 206) of the on-line version of Sean Carroll's book...,

Thanks, George. I'm afraid I'm not very good at interpreting Penrose diagrams, but I now have Carroll's lecture notes and may acquire this skill in time.

I take it from your comments that the event horizon is indeed something invisible to remote observers, which nucleates and dilates from a singularity that is characterised by infinitely strong tidal forces. I'm still a bit baffled by the concept of such a process occurring with (to us) an eternally frozen horizon to create black holes that we accept as "existing" now.

 

[oldman]

I've had a while since writing my OP to read what Sean Carroll wrote about the formation of black holes, to look at recent threads and other references about black holes and to consult with a colleague who is an active researcher in GR about the problem I have, namely how black holes get to be or, more precisely, how an event horizon starts from zip.

I now understand why there has been only one reply to the OP (courtesy of George Jones).

Nobody seems to have a clue.

Sean Carroll's simply says that "it is believed that the inevitable outcome (of the collapse of a neutron star) is a black hole" (p.192 of PDF) and then returns to discussing the utility of various coordinate transformations in describing succintly the spacetime of the Schwarzschild geometry.

Physics FAQ does ask:Won't it take forever for the black hole to even form? but gives only the answer "If you attempt to witness the black hole's formation, you'll see the star collapse more and more slowly, never precisely reaching the Schwarzschild radius." which begs the question of how "the Schwarzschild radius" got to be there in the first place. This is the question I'd like to have answered.

Texts (such as Rindler's Essential Relativity) treat the event horizon as a somehow pre-existing reality which simply "is" and which can be discussed and described with coordinates, even though this presents in principle an operational impossibility.

It all depends on one's viewpoint, I suppose. When you discuss things that are, it seems generally accepted that in this universe they cannot have existed, from our perspective, for more than about 13.7 billion years. This implies that if the nuclei of event horizons took an infinite time to form, as GR tells us from our perspective is the case, they can't yet be there!

I'm back to thinking of black holes as wanna-be singularities that don't yet exist. As my informed colleague puts it: "the objects that go by the name of "black hole" are super-dense bodies that hover just short of forming an event horizon. The older they are the closer they come, but they never actually get there." I just wish that people would stop talking and theorising about things that as far as we are concerned, can't yet exist.

 

[Ich]

You can find some information in http://arxiv.org/abs/gr-qc/0506119" , but you'll first have to figure out much of the concepts (different definitions of horizons and so on.

However, I'm quite sure that the horizon starts with regular curvature at some perfectly normal event.

 

[oldman]

You can find some information in http://arxiv.org/abs/gr-qc/0506119" , but you'll first have to figure out much of the concepts (different definitions of horizons and so on.

However, I'm quite sure that the horizon starts with regular curvature at some perfectly normal event.

Thanks, Ich. This reference looks at last like something I can learn from, although they seem to be concerned mainly wth accretion onto pre-existing black holes. I'm concerned with how these objects get to be pre-existing in the universe we see, in the first place. As you say, it'll take me some effort to figure their approach out.

Your last sentence suggests that you have opinions about how black holes get started. Would you care to amplify your thoughts? A fuller description would be welcome in the meantime.

 

[George Jones]

You can find some information in http://arxiv.org/abs/gr-qc/0506119" , but you'll first have to figure out much of the concepts (different definitions of horizons and so on.

The first author of the above paper (whom I have met) has written a review paper,

http://arxiv.org/abs/gr-qc/0508107.

 

[Ich]

although they seem to be concerned mainly wth accretion onto pre-existing black holes.

No, they have a long section dealing with a collapsing dust sphere. Chack out fig. 3, where they comment:

This diagram also nicely shows that while the MTT appears at the same time as the singularity, nothing in particular is happening at r = 0 when the event horizon “appears”.

Your last sentence suggests that you have opinions about how black holes get started. Would you care to amplify your thoughts?

Sorry, not much to amplify here. I read some times ago about the different definitions of horizons and how they behave. For example: the horizon grows before new matter falls in. Unfortunately, I forgot the source.
But from what I remember, and from the qoute above, it seems the the EH appears long before the singularity - which makes sense, if you think about it.

EDIT: George Jones, that's the paper I'm talking about. Thanks!

 

[George Jones]

Yes, the tidal forces at the event horizon start off at infinity (horizon and physical singularity together) and progressively diminish as the star is swallowed. For a Penrose diagram of black hole formation from spherical stellar collapse, see page 199 (pdf page 206) of the on-line version of Sean Carroll's book,

http://xxx.lanl.gov/abs/gr-qc/9712019.

However, I'm quite sure that the horizon starts with regular curvature at some perfectly normal event.

I was mistaken, and Ich is correct, as the diagram to which I referred clearly shows! I had a different, incorrect diagram pictured in my mind, and I didn't look carefully at Carroll's diagram. This is shown perhaps even more clearly in the two diagrams at the bottom of page 155 (pdf page 171) of Eric Poisson's notes (also the basis for a book),

http://www.physics.uoguelph.ca/poisson/research/agr.pdf.

 

[oldman]

The 2005 review by Booth that you pointed me to, George, is (almost) intelligible to me and is very helpful. Thanks. It seems as if the formation of b.h.'s has received more attention than I'd ever dreamed of. Ignorant me. But my original thoughts seem to have been along the right lines, namely that the event horizon first forms at the centre of the collapsing object and then propagates outward through the infalling matter:

Then, we can trace the evolution of this (event horizon)
surface backwards in time to find its orgin at r = 0. We note that there is nothing special happening at r = 0 at that point. Instead the event horizon appears in anticipation of future events ... ...equations (given in the article)...guide its evolution as we follow it forwards in time. The newly formed horizon exists in vacuo and ...(its) rate of growth ... is positive and accelerating. This continues until the first shell of matter crosses the horizon...

But when does the e.h. form, as judged by an observer in an exterior FLRW universe, if he is observing the collapse (of say a neutron star), as a function of "universal time" (which he deems to be a good enough approximation to a more precise, complicated and correct foliation) ?

Is "never" the short answer?

If it is, how can gravity waves from the formation of the b.h. (however this "process" is timed) ever reach an observer whose clocks measure G.M.T? I'm still a bit adrift here, not yet understanding how the analysis can be relevant to possible physical observations.

 

[Chronos]

Gravity is a top down process. It can be emitted by black holes because it originates from outside the singularity.

 

[JohnnyRock]

Gravity is a top down process. It can be emitted by black holes because it originates from outside the singularity.

Are you sure? Gravitons (if they exist) and photons are both massless particles. Black holes have gravitational fields strong enough to prevent anything from escaping the Schwarzschild radius. Shouldn't this include both gravitons and photons?

 

[oldman]

Are you sure...

I have come to the conclusion that as far as b.h.'s are concerned, people who have in this fashion described the unexplored and extreme concentrations of mass/energy that populate the centres of galaxies are not at all sure about any aspect of these mysterious regions. This procession of overconfident theoreticians starts with Schwarzschild, continues through a succession of astrophysicists too illustrious to denigrate, and ends with today's diligent but deluded cohort of paper-writing and conference-attending b.h.theorists.

How can one possibly be sure about the genesis and details of a process that is thought to happen only at the end of eternity?

William Gilbert had it right when about four hundred and ten years ago he wrote:

In the discovery of hidden things and in the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort

And of the uncommon sort.

 

[Ich]

So it took you 5 days from being adrift, not yet understanding and almost being able to read the first review paper on the subject you encountered, to knowing enough to ridicule the cohort of deluded theorists?

Either we're witnessing a miracle here, the steepest learning curve in history, or just the next one who likes to rail at something without knowing what he's talking about.

 

[oldman]

So it took you 5 days from being adrift, not yet understanding and almost being able to read the first review paper on the subject you encountered, to knowing enough to ridicule the cohort of deluded theorists?

Either we're witnessing a miracle here, the steepest learning curve in history, or just the next one who likes to rail at something without knowing what he's talking about.

It was a steep learning curve ending in disillusion rather than knowledge, Ich.

When I first asked how event horizons nucleate I thought that this would be a matter for a knowledgeable person, like you, perhaps, to explain simply to someone who doesn't know much about black holes ---- like myself (as you recognise so pungently, Ich). But it seems that a straightforward answer is not to be easily obtained here.

In the review by Booth I was kindly referred to, at the end of section 2.1 he writes:

This means that it (a Schwarzschild b.h) is a highly non-local object as its very existence depends on the structure of infinity. Second, even if the spacetime has the correct asymptotic structure we must still wait until “the end of time” to locate the event horizon. It cannot be identified by local measurements.

.

It then seems that from the perspective of remote observers my original question will never be answered. So far so good, even if disappointing. But Booth's later contention (start section 5) that:

Perhaps the most basic motivation for the study of quasilocal horizons (which is the main theme of Booth's review, too technical for me) is the philosophy that black holes should be thought of as physical objects in a spacetime which may be identified and quantified by local measurements.

brought disillusion.

Who could possibly be thought of as carrying out a local measurement in such a place? And when, as we judge time? This is mere sophistry.

And why should any physicist bother to have a "philosophy" about black holes if measurements and observations that could either confirm or reject their existence, or the validity of proposed alternative characterisations, is impossible --- even in principle?

And why, in writings about b. h.'s and their event horizons, is their inception and evolution so often ignored ( in the Schwarzschild analysis as commonly presented), and not treated, even if only to say that it is a mystery too esoteric to be understood by the uninitiated?

The silence of yourself and other researchers tells the correct story, Ich.

 

[Ich]

as you recognise so pungently

I used your own words.

The silence of yourself and other researchers tells the correct story, Ich.

I told you what to do first:

you'll first have to figure out much of the concepts (different definitions of horizons and so on

If you even bothered to learn how an event horion is defined, it would be clear to you why Booth calls it a "nonlocal object". And it should come as no surprise to you that you can't locally measure an EH, just as you can't find the midpoint of the United States (or wherever you come from) by walking around and looking for it (unless someone thought of placing an according sign there). If you find such concepts disturbing, well, you got to learn that this is not necessarily a sign of the people talking about it being clueless. It could also be you.

 

[George Jones]

oldman, let's forget GR for a bit and only consider 1+1 SR. Fix a particular inertial reference. With respect to this frame, the worldline of observer A is given by

t = tau_A
x = 2.

With respect to the same inertial frame, the worldline of observer B is given by

t = sinh(tau_B)
x = cosh(tau_B).

Is there anything problematic about this situation?

 

[oldman]

...
Is there anything problematic about this situation?

No.

But I do hope this the start of a tutorial that's going to teach me how event horizons evolve from zip to say 10^7 km across in what we measure as less than say 10^8 years!

I look forward to more. Thanks, George.

 

[George Jones]

I don't think this is going to make you any more comfortable with respect to black holes.

Observers A and B are coincident at

(t , x) = (sinh(cosh^-1 (2)) , 2),

after which they move apart. What does B see as he watches A (through a telescope) move away?

 

[oldman]

I don't think this is going to make you any more comfortable with respect to black holes.

Observers A and B are coincident at

(t , x) = (sinh(cosh^-1 (2)) , 2),

after which they move apart. What does B see as he watches A (through a telescope) move away?

A gets smaller and redder as B is boosted and reaches a steady velocity, I guess. But why B looking at A? It's A's home frame, as it were. I'm still in the dark as to where you're going with this, George ... but let's see.

 

[oldman]

Hello, George. Thanks for your attempt to lead me, via what seems to be a kinematic description of a boost in one dimension, to an appreciation of the meaning of an asymptotic approach to c via the function tanh. Or perhaps I've misunderstood you. No matter. Thanks.

Thanks also for opening a door to considering one-space-dimension models, as with your "1 + 1 SR". Have you ever thought about what "1 + 1 gravity" could teach us about GR?

GR tells us that gravity is a manifestation of the "curvature" of spacetime, (rather mysteriously) induced by the presence of mass/energy. Now curvature, as we usually think of it, needs three spatial dimensions to be appreciated by uninitiated folk lacking a knowledge of the Riemann tensor. As in the curvature of the Earth's surface, often used as a didactic crutch, or the curvature of a bimetallic strip in a heat sensitive switch.

An aspect of spatial distortion described by components of the Riemann tensor is the spatial expansion of the universe, so puzzling for those new to modern cosmology. The number of threads about such expansion in these forums shows that the universe's evolution-by-expansion is not easy to grasp.

But in a "1 +1" --- one-space-dimension --- model it is not sensible to describe a spatial distortion by mass/energy as "curvature". Here the only possible description is a distortion of scale --- expansion or contraction. Such a model therefore concentrates attention on what exactly is meant by expansion. Here it is change from place to place along a line of (I guess) the spatial metric coefficient (implicitly set to invariant unity in the metric of SR). But relative to what is this coefficient gauged? I guess again: relative to another metric coefficient. The only one available in this restricted case is the time coefficient (again implicitly set to invariant unity in SR).

This tells us, I think, that it is the ratio of these two metric coefficients that must be changed by the presence of mass/energy in one dimensional gravity. I have long since found this interesting .

 

[jambaugh]

Let's consider a black hole forming as smoothly as possible. Suppose you have a neutron star which is almost dense enough to form a black hole. Say its pretty hot but cooling down and very slowly contracting. From outside you'll see the thermal spectrum of the neutron star dramatically red-shifted.

Now as it cools it contracts enough that the inner density forms an event horizon just a bit below the surface. It won't generally start at the center but manifest partway between center and surface. As the neutronium outside falls inward it expands until all the neutron star is inside.

From outside you'll see the outer surface of the neutron star falling inward taking infinite time (but finite proper time) and as it does it will redshift off the scale. At some point (assuming Hawking is correct) you'll see the thermal spectrum of the event horizon "outshine" the red-shifted thermal spectrum of the infalling matter. But of course this will be much colder than the cosmic background.

I guess technically we never exactly see all the way to an event horizon of a conventional black hole since the matter infalling from the time of its formation will from our perspective take forever to finally fall past the horizon due to gravitational time dilation. It's something of a moot point though as you see a black sphere in any event surrounded by a halo of distortion due to gravitational lensing. (And in typical real examples a very very hot accretion disk of infalling matter with x-rays and energetic particles jetting out the poles.)

But the event horizon doesn't "nucleate" as such. It manifests as a boundary, not as a physical object. It's no different in quality than say when you bend a piece of paper as you look at it obliquely. At first you see the whole sheet though obliquely. Then at some instant the curvature is sufficient that there is a horizon you can describe on the sheet beyond which the surface is obscured from your line of sight. Nothing change about the paper as this instant passes except that a relationship between observer and paper changes qualitatively. Of course the dynamic implications of the event horizon's manifestation is more dramatic but the nature of its formation is no different. It just suddenly becomes well defined.

 

[oldman]

Let's consider a black hole forming as smoothly as possible...

... the event horizon doesn't "nucleate" as such. It manifests as a boundary, not as a physical object. It's no different in quality than say when you bend a piece of paper as you look at it obliquely. At first you see the whole sheet though obliquely. Then at some instant the curvature is sufficient that there is a horizon you can describe on the sheet beyond which the surface is obscured from your line of sight. Nothing change(s) about the paper as this instant passes except that a relationship between observer and paper changes qualitatively. Of course the dynamic implications of the event horizon's manifestation is more dramatic but the nature of its formation is no different. It just suddenly becomes well defined.

This is exactly the kind of reply to my O.P. I'd been hoping for, jambaugh. Of course a horizon is "a relationship between observer and paper", as you say. Not something physical. I should have thought more clearly about this. Thanks very much.