Value of g near a black hole (re-visited)

questionpost

So then we could never tell when a black hole at least is about to gain mass. We shouldn't expect any changes of the black hole if we never see anything going into it, other than perhaps its velocity. Also, what's the point of saying time stops to us at the event horizon if we can just easily calculate how matter travels past the event horizon? Why so many debates if it's that simple?


How does the event horizon, which is symmetrical to the singularity, expand before matter has reached the singularity? Wouldn't that imply the object and the singularity are the same object if they have the same gravitational field? Why does there even need to be a bulge that straightens out? It's just something with it's own little field that clearly doesn't have the same capabilities of a black hole, I don't see how it would effect the size event horizon unless it also had an escape velocity greater than light.

PAllen

There are no debates within GR (about these basic issues; of course there are about some issues). There is only difficulty understanding that time and simultaneity are observer dependent. "Time slows to a stop for an infaller" is a statement that should always be joined to: "from the point of view of a static observer further away; not from the point of view (for example) an infaller just ahead of a given infaller".
How about some nice pictures:

http://www.black-holes.org/explore2.html

search, e.g., for merging event horizons.

PeterDonis

Did you read my post #33? You are assuming that the "mass" of the black hole is somehow "located" at the singularity, and doesn't increase until the infalling object arrives there. That is false.

Nabeshin

Yessss, more traffic for our website :P

pervect

Yes, sorry if this wasn't clear. A stationary observer is basically an observer with constant r, theta, and phi Schwazschild coodinates.

In order to qualify as an observer, his worldline must be timelike. (Which is another technial term from special relativity). An photon isn't an observer, for instance.

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I don't see why you say it's misguided. Though I think it may be confusing the OP, because Thorne's approach isn't based on the "clock slowing" paradigm.

My basic impression is that the OP is stuck in a Newtonian view of absolute time, and is also interpreting the whole "clock slowing" down thing as some sort of scalar function that modifies how fast absolute time flows at a given position.

And this is just not compatible with special relativity at all (mostly because of the absolute time idea).

At the risk of possibly causing more confusion, Thorne's view is more like saying that the time doesn't really "stop" (as per the stopped time idea), it's just bent to point in a spatial direction.

questionpost

Ok, when black holes merge, then I see how the event horizon increases, however I don't see how a *not* infinitely dense object does the same thing, so shouldn't the object first have to have an infinite density like the singularity in order to have an event horizon and then merge that event horizon with the black hole its falling into? And since it can only have an infinite density by merging with the singularity, shouldn't the even horizon not increase until then even if the gravitational pull does?

Ok, then "why" does it stop just because it's at a boundary where the escape velocity happens to be light? Also, you said before that other escape velocities don't matter, so does that mean once inside the event horizon, even if I traveled 99% the speed of light away from the singularity, it wouldn't slow down my in-fall? It seems related to hypothetically traveling at the speed of light.
Why is that too? We can calculate what happens when you travel at the speed of light with an equation yet right next to it have another equation that says you can never travel at or faster than the speed of light, within the same theory known as GR.

PAllen

Well, time pointing in a spatial direction is a non-sequitur. At any point in a manifold there is a light cone defining time like directions, light like directions, and space like directions. Any small region looks just like Minkowski space, including a region where the horizon is passing by at c. There is nothing spatial about a timelike direction inside an event horizon except that it is labeled r in some coordinate schemes. It's labeled U or V in Kruskal (depending on your convention). It's labeled t in local Fermi-Normal coordinates. I think it is genuinely misleading to attach significance to a letter used in interior Schwarzschild coordinates for what essentially are historic reasons.

PAllen

Why? That's not really a question of physics. A distant observer would see a a clock slow and light red shift on approach to a neutron star. Approach to a horizon is the same thing only more extreme. Asymptotically stopping just reflects that force needed to escape becomes infinite on approach to horizon. This stoppage is only observed by someone remaining further away from the horizon. There is no stoppage for the infaller.

I don't know what you are referring to in claiming I said escape velocities don't matter. I don't know what you are going on about traveling at or faster than the speed of light. I keep repeating this is all nonsense.

The singularity is a point in time not in space. Once inside the horizon, you can shine a flashlight any direction, and fire bullets in any direction, but all light and any projectiles you fire, in any direction, move forward in time toward the singularity. Poetically, you can say the singularity is a point in time where space ceases to exist for you. (In fact, you will be subject to enormous (ultimately infinite) compression and stretching, but you can always define a tiny enough region where everything is momentarily normal - until the moment of reaching the singularity).

pawprint

The OP thanks you all. This has been a most interesting thread and I have achieved the desired 'intuitive' breakthrough that I was seeking. Just a few notes in special appreciation starting with post #16-

I've been quite comfortable with the implications of SR for about 37 years now pervect. I like your analysis but you made an error in the first paragraph.

I won't quote quotes but I found the two in post #19 by Naty1 very helpful. In Post #20-

questionpost has expressed the same thought that has been concerning me for a long time, and which prompted this thread. But I'm no longer concerned. The answer I have found from the many responses is that although observers see objects slow effectively to a stop before passing the event horizon, the observation is dependant not on a single effect (time dilation) as I had previously thought but also on gravitationally caused 'slowness of light' from the object back to the observer.

The same statement rephrased: Were an 'instantaneous' link available from the falling clock to a slave clock held by an observer, it would indeed show the falling clock to be slowing at a rate depending on the gravitational gradient of the particular black hole. BUT IT WOULD NOT SLOW TO ZERO at the event horizon. The appearance of this effect to an observer without a simultaneous link, while real enough, is caused by the slowness of light (or other EM signal) returning to the observer from the intense gravity field. The 'simultaneously' linked clock would only approach zero rate of change as it approached the singularity.

The clock itself behaves exactly as it would aboard a vessel approaching light speed, with all the same implications for local and distant observers. After all, although nothing can be seen to 'break' the speed of light this doesn't change the fact that an intrepid traveller accelerating at 1 g will subjectively do so after about three years.

As I have said before, I seek intuitive understanding without math. Of course I know that simultaneous links are thought to be impossible, and that infinite anythings are rare. Indeed the only infinite 'physical' thing I can think of is the depth of a gravity well in which sits a singularity.

Once again thanks to everybody who participated in this thread. You have settled demons which have been of growing concern to my intuition for some time.

pawprint

OP here again. Not having refreshed my browser I had missed this quoted post. I now must take issue with paragraph 1-
I now hold the view expressed in the previous post that the clock does not asymptotically stop at the event horizon, it only LOOKS as though it does...

PeterDonis

Your picture of a black hole is not an accurate one. Several issues:

(1) The "black hole" is not just the singularity. The term is used to refer to the entire region of spacetime inside the event horizon. When people talk about two black holes merging, they are talking about two regions inside event horizons merging into one region inside an event horizon.

(Strictly speaking, there is only a single event horizon, and only a single region of spacetime inside it; that region just happens to be shaped like a pair of trousers instead of a tube, so to speak.)

(2) A black hole is not "infinitely dense". The singularity itself can be thought of as "infinitely dense", but the singularity has no causal effect on anything else in the spacetime, so its characteristics are irrelevant for understanding what happens elsewhere.

(Strictly speaking, the singularity is not even "in" the spacetime--the spacetime itself "ends" at the singularity, meaning there are events arbitrarily close to the singularity but none actually "at" it.)

(3) The event horizon is defined "teleologically"--it is the boundary of the region of the spacetime (as above, there is only *one* such region, but it may be shaped like a pair of trousers instead of a tube) that cannot send light signals to "infinity" (strictly speaking, to "future null infinity"). That definition requires you to know the entire history of the spacetime to pin down exactly where the horizon is. So when an object of non-negligible mass falls into a black hole, the horizon starts to move outward from its old radius to its new radius even *before* the infalling object reaches it, because the horizon is defined in terms of where light signals go all the way into the infinite future. A light signal sent from outside the "old" horizon radius may still be trapped behind the new horizon even if it is sent *before* the infalling object reaches the "new" horizon radius--if it is sent a short enough time before, so that it doesn't have time to make it past the new horizon radius before the infalling object arrives.

Take a look at the diagrams on this page:

http://casa.colorado.edu/~ajsh/collapse.html

Particularly the Kruskal and Penrose diagrams of the star collapsing to a black hole. It may help to visualize what I'm saying above.

pawprint

That's a great page PeterDonis, and it entirely confirms my new paradigm.

PAllen

I don't understand what you disagree with, but a fact is that the whatever you say about a clock sitting in a dense planet or neutron star (gravitational time dilation and red shift) you must say the same thing about a clock hovering near the event horizon, because they are exactly, in every way, the same phenomenon in GR. Note that a clock hovering near the event horizon sees distant clocks going extremely fast. An infaller is different because (see Pervect's post a little earlier) because you have SR speed effects as well as gravitational time dilation.

pawprint

There is one significant difference PAllen. The VIEW of the clock sitting on a neutron star is not subjected to the near 100% redshift that the clock near the event horizon is.

PAllen

It is just a matter of degree. The clock on the neutron star is extremely redshifted. If more matter fell into the neutron star until it collapsed into a black hole, the redshift of the clock would smoothly grow arbitrarily large (assuming it maintained position on the collapsing surface, then hovers just outside the freshly formed event horizon). The phenomena are absolutely identical in GR. You cannot claim they are different (except for degree) unless you reject GR - in which case you should say so.

pawprint

Clarification:

A clock near an event horizon would appear to have slowed to almost nothing, considering red-shift alone and excluding gravitational effects. In 'reality', as far as it can be applied in these circumstances, the gravitation slows the clock to near zero at the singularity. The redshift, by different means, makes the clock appear to have stopped at the event horizon.

PeterDonis

This statement doesn't even have a well-defined meaning. There are no "static" observers inside the horizon; that is, no observers who "hover" at a constant radius. So the interpretation of "rate of time flow" that works outside the horizon, and according to which a clock "hovering" near the horizon "runs very slow" compared to a clock far away, does not even work inside the horizon. Unless you can come up with some alternate way of comparing the "rate of time flow" near the singularity with that far away from the hole, you can't say anything at all about how gravitation "slows clocks" near the singularity.