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

[PAllen]

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?

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 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?

How about some nice pictures:

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

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

 

[PeterDonis]

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?

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]

How about some nice pictures:

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

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

Yessss, more traffic for our website :P

 

[pervect]

None of these are contradictory, though Thorne is at least misleading in an attempt a drama.

Let's take them one at a time:

"There is no such thing as a stationary clock at the event horizon." Here, you are rather naturally confused by ambiguity in English language. Pervect is here referring to stationary in the sense of motionless relative to distant observers, not rate of time flow on a clock. The two senses of stationary juxtaposed this way lead to false perception of contradiction. Sorry about that. English is a ... <forum rules> sometimes.

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.

Thorne's comments about "a direction you would have thought was spatial" and a "downwards direction" are misguided. The only one expecting this would be someone who interpreted coordinates according the letter used to name them rather than their physical characteristics.

]

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.

In standard Schwarzschild coordinates, the coordinate called 'r' is spacelike outside the horizon and timelike inside the horizon. This means nothing except that 'r' is a bad label for the coordinate inside the horizon. If you instead use the local Fermi-Normal coordinates of a infaller, all of this nonsense disappears.

 

[questionpost]

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.

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?

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

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]

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.
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.

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]

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.

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-

A stationary clock near a singularity would run slow when compared with another stationary clock that's far away from any singularity, and it'd approach stopping as the stationary clock got closer and closer to the event horizon.

There's no such thing as a stationary clock at the event horizon, however. In fact, any clock crossing the event horizon must be moving at the speed of light - or rather, since the event horizon can be thought of as trapped light, any physical infalling clock, which is stationary in its own frame, will see the event horizon approaching it at the speed of light.

This motion causes signficant SR effects. If you neglect the velocity effects, it would be correct to say that from the point of view of an infalling observer, a clock at infinity would run faster and faster, without bound, as one approached the event horizon,.

When you include the velocity effects, though, the clock at infinity doesn't run infinitely fast.

You will run into the usual special relativity (SR) issues associated with the twin paradox when you include the velocity effects - I'm not sure what yoru background is in SR.

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-

...It doesn't even make sense that time would stop, because then how would anything ever reach the singularity to add to its mass?

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-

...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 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]

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?

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]

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.

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

 

[PAllen]

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...

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]

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.

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]

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

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]

In 'reality', as far as it can be applied in these circumstances, the gravitation slows the clock to near zero at the singularity.

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.

 

[pawprint]

...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.

I have (see post #43). I'm sorry you don't agree. And I don't dispute GR.

 

[PeterDonis]

I have (see post #43). I'm sorry you don't agree. And I don't dispute GR.

That's good (meaning not disputing GR). But your post #43 does not propose a valid way of defining "rate of time flow". Here is what I take to be the relevant part of your post #43, with comments interspersed:

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.

For the "rate of time flow" of a *static* observer hovering close to the horizon, this viewpoint works OK. It does *not* work (at least, not as stated) for the "rate of time flow" of an observer falling *into* the hole.

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.

Here you are trying to reason about the "rate of time flow" of an infalling clock, but you are depending on this idea of an "instantaneous link" between the infalling clock and a "slave clock" hovering far away. But you haven't defined *how* this "instantaneous link" is specified--in other words, you haven't told me, if I'm looking at a spacetime diagram of the hole, showing the worldlines of the infalling object and the "slave" clock, how to draw "lines of simultaneity" between them to define which pairs of events are "linked" by the instantaneous link. Once you do that, then you can try to define a "relative clock rate" that way; it still won't work, but at least you could try, and perhaps trying it will help you to see the problems.

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.

No, it wouldn't. See comments above; this is one of the things that might become more evident to you if you actually tried to explicitly define a "simultaneous link".

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.

You have this backwards. From the standpoint of GR, the *hovering* clock--the clock that is static at a constant radius r, above the horizon--is the one that is "accelerating". The observer that is freely falling into the hole is not "accelerating" at all; he's in free fall. So if you are trying to make an analogy with an observer accelerating in a rocket, that observer is analogous to the *hovering* clock, *not* the infalling clock.

 

[pawprint]

Others have spoken of infalling observers and I agree with them unconditionally. I also agree with eveything you said about them in your last post. But I have not mentioned them in this thread.

As for the "instantaneous link" it will be a sad day for physics when thought experiments are disallowed.

 

[PAllen]

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.

This is factually wrong. Gravitational time dilation and gravitational redshift are the same phenomenon. There is no redshift for a clock hovering near the the horizon that can be separated or distinguished in any way from the redshift of a clock sitting on a neutron star (except for degree). These are mathematical facts, not subject differences of opinion.

 

[pawprint]

This is factually wrong. Gravitational time dilation and gravitational redshift are the same phenomenon. There is no redshift for a clock hovering near the the horizon that can be separated or distinguished in any way from the redshift of a clock sitting on a neutron star (except for degree). These are mathematical facts, not subject differences of opinion.

I know it does not fit the current paradigm. Let me try it another way: Only an infinitely deep gravitational well slows clocks infinitely. The well at the event horizon is not infinitely deep. It is certainly less deep than at the singularity. You are effectively asserting that clocks are slowed infinitely by gravity equivalent to the escape speed of light.

 

[PAllen]

I know it does not fit the current paradigm. Let me try it another way: Only an infinitely deep gravitational well slows clocks infinitely. The well at the event horizon is not infinitely deep. It is certainly less deep than at the singularity. You are effectively asserting that clocks are slowed infinitely by gravity equivalent to the escape speed of light.

It is precisely infinitely deep in the sense that the thrust required to escape from near the horizon goes to infinity as you approach the horizon. This 'escape thrust' requirement is the exact equivalent of g force on a neutron star, extrapolated to the limit. Inside the horizon, there is no escape at all, and no ability to define a reasonable notion of g force. Note an earlier post, where I described that progress toward the singularity inside the horizon is progress in time, not toward a spatial point. Shoot a bunch of bullets away in all directions, and they will move away from you in all directions (spatially), while all move forward in time towards the singularity.

 

[PeterDonis]

Others have spoken of infalling observers and I agree with them unconditionally. I also agree with eveything you said about them in your last post. But I have not mentioned them in this thread.

Yes, you have, though you may not have realized it. You talked about observers approaching the singularity. Such observers *have* to be infalling; there are no timelike (or null) worldlines inside the horizon that do not move continuously inwards towards the singularity.

As for the "instantaneous link" it will be a sad day for physics when thought experiments are disallowed.

I wasn't disallowing your thought experiment; I was pointing out that it was incompletely specified, and saying what a proper specification would have to look like.

 

[pawprint]

OK. The difference between the Senior members and myself is spacetime related, and furthermore is now well defined. It need not be restated here. I think we can all agree on at least that much :{)

The generally agreed position is that we, in the 'external' universe, cannot observe a clock, or anything else except perhaps another black hole, enter an event horizon in finite time, let alone 'rapidly'. I think this position has been locked in pretty firmly by PAllen, PeterDonis and others. This position necessarily implies that gravitational wave detectors can never detect such events.

Given this I think it reasonable to consider two cosmological implications of the agreed view.

1) Several billions of dollars have been spent on gravitational wave antennas. At least some cosmologists (a large majority, perhaps) expect the antennas to detect black hole events within their limit of sensitivity. If the Senior forum members are right then those cosmologists are mistaken. The events will occur so slowly (in relation to the detectors) that the detectors will at best see them, in electomagnetic terminology, as smoothed DC.

2) The current cosmological paradigm assumes that black holes have grown in the past and continue to grow today. What alternatives exist? Did they all spring out of the primal event full blown?

A deep dichotomy is felt. The insight (or madness perhaps) I am defending agrees with the cosmologists' expectations. I cannot see how the opposing view can accommodate them.

My position has not changed since my opening post, but it has certainly become better defined from a cosmological perspective. Perhaps it would be more appropriate for a new thread to be started, possibly in a different forum, if members would like to continue in this new cosmological vein. Would a Senior member like to adjudicate (or arbitrate) on the proposition? In the meantime we can perhaps agree on a clearly shared opening position here.

Thank you all.

"Disability access is a Dalek Plot"

 

[PAllen]

The generally agreed position is that we, in the 'external' universe, cannot observe a clock, or anything else except perhaps another black hole, enter an event horizon in finite time, let alone 'rapidly'. I think this position has been locked in pretty firmly by PAllen, PeterDonis and others. This position necessarily implies that gravitational wave detectors can never detect such events.

No, it does not imply that. Whether a star is torn apart and mostly absorbed by a black hole, or two black holes merge, enormous gravitational radiation (GW) will be emitted. It's (the GW) energy content will often carry away over 5% of the total mass of the star or black hole. There is no contradiction because the GW is generated by activity outside the initial event horizon. Further, the enlarged event horizon 'rings' for a while, emitting more GW. These are all oscillations of the metric (or geometry) outside the event horizon.

Given this I think it reasonable to consider two cosmological implications of the agreed view.

1) Several billions of dollars have been spent on gravitational wave antennas. At least some cosmologists (a large majority, perhaps) expect the antennas to detect black hole events within their limit of sensitivity. If the Senior forum members are right then those cosmologists are mistaken. The events will occur so slowly (in relation to the detectors) that the detectors will at best see them, in electomagnetic terminology, as smoothed DC.

There is no disagreement. See above. These are difficult concepts. The only 'issue' is your level of understanding, which you are trying to improve - great!.

2) The current cosmological paradigm assumes that black holes have grown in the past and continue to grow today. What alternatives exist? Did they all spring out of the primal event full blown?

Models for the formation of stellar black holes are pretty well defined. At present, there are more unknowns, than knowns, about how supermassive black holes came to be. This is an active research area. However, no one believes they are primordial; they grew somehow; it is just that models so far don't show a likely way for the big ones to form.

A deep dichotomy is felt. The insight (or madness perhaps) I am defending agrees with the cosmologists' expectations. I cannot see how the opposing view can accommodate them.

My position has not changed since my opening post, but it has certainly become better defined from a cosmological perspective. Perhaps it would be more appropriate for a new thread to be started, possibly in a different forum, if members would like to continue in this new cosmological vein. Would a Senior member like to adjudicate (or arbitrate) on the proposition? In the meantime we can perhaps agree on a clearly shared opening position here.

Thank you all.

"Disability access is a Dalek Plot"

No need for a new thread. The discussion here is going fine, and I hope is helpful.

 

[PAllen]

Let's be clear about one thing. The statement that no one outside the horizon sees, or is causally influenced, by anything inside, does not imply that nothing exists inside. Let me describe Rindler horizon scenario. Two ships are accelerating together at 1 g for a long time. They have reached extremely near c. One of them runs out of fuel and stops accelerating. The other ship will see the out of fuel ship fall a little behind, but then become red shifted, clocks on it slow down and asymptotically stop; red shift grows to infinity.The empty ship becomes invisible. The empty ship is never seen to be farther than a short distance away from accelerating ship, as long as it can be seen at all. It is 'trapped' on the Rindler horizon. Of course, for the empty ship, nothing strange has happened. The other ship accelerates away from it, getting ever further away. The empty ship can receive signals from the accelerating one, but any signals it sends can never reach the accelerating ship (because the accelerating ship stays ahead of the light; no contradiction because it had a head start and keeps accelerating - no superluminal implication).

This scenario has much similarity to the black hole event horizon.

 

[PeterDonis]

The generally agreed position is that we, in the 'external' universe, cannot observe a clock, or anything else except perhaps another black hole, enter an event horizon in finite time

There's another distinction here that you are not making, which I think I have mentioned, but which it's worth making explicit. The model that says that light from an object falling into a black hole will take longer and longer to get out to a distant observer (until ultimately light from the object just as it crosses the horizon takes an "infinite time" to get out to a distant observer) only applies, strictly speaking, to a "test object" falling into the hole. That is, it only applies if the mass of the object falling in is so small that any effect its mass has on the curvature of the spacetime as a whole is negligible. The scenarios we have been discussing here, where two black holes merge, or where an object of non-negligible mass (such as a star) falls into a black hole, do not meet this requirement; so strictly speaking, the argument that it will seem to take an "infinite time" for an object to reach the horizon, according to a distant observer, does not apply to these scenarios.

It is still true that light from events near the horizon takes longer to get out, even in the scenarios we have been discussing. But the fact that the infalling objects are of non-negligible mass means that the horizon's radius changes during the process, which changes the rules, so to speak, that determine what information can escape.

 

[pawprint]

I submit. I set a trap for the Seniors and it has been turned upon me.

In my last post I brought real black holes (as opposed to ideal ones which are likely to be rare) back into play by resorting to cosmological arguments. I can find no fault in PAllen's response. Once again I have to agree with everything said in reply, or at the least admit I cannot combat the arguments. I cannot feel comfortable with any description of gravity except 'that which locally distorts spacetime'. The only way I'll win this argument is if my view is supported by gravitational observations, which so far are non-existent.

Indeed it is the sublime silence of LIGO which has brought me into the gravitational fray over the last couple of years. But that's another thread. I have been interested in gravitation as distortion of spacetime for a long time, and it has become important to me to better understand as many of its implications as I can manage.

Overnight (for me) I see PeterDonis has also posted. Thank you PD. I specifically had that point in mind when I included 'or anything else except perhaps another black hole' in my last post. I'm glad you pointed out that the exception applies to all non-negligible masses.

There is only one (non-mathematical) point from the entire thread that I have not truly grasped. I accept the concept that, as almost infinite energy is required to hover near the event horizon, gravity can be inferred to become infinite at the EH. My difficulty is that the singularity must be at a more distorted (i.e. deeper, in the image below) position in spacetime than the event horizon, and if this is so then spacetime at the EH cannot truly be said to be infinitely warped. I alluded to this when I spoke of the intrepid explorer subjectively exceeding the speed of light.

My problem may simply be due to the impossibility of representing spacetime in three dimensions.

(This image is believed to be unencumbered by copyright)​

My memory is that not many years ago such diagrams of black holes showed an infinitely deep gravity well at the singularity. However now a search reveals the vast majority of such images to resemble that shown here, with almost flat bottoms. Does this represent a paradigm shift or just lazy artists?

 

[pawprint]

A quick addition to my last post. I don't dispute GR but neither do I believe it to be a complete theory yet. I expect a new class of experiments will shake a few ideas within the next decade. In particular I expect the constancy of G to be seriously questioned. If G is not constant either in space or time then all inferences from astronomical observations will need to be reconsidered.

 

[pervect]

The curvature of space-time is non-singular at the event horizon. Being a bit more specific, we can say that the tidal forces on a body freely falling through the event horizon are finite. They're calculated in most textbooks, for instance you'll find the detailed calculations in MTW if you look. The tidal forces on a free-falling body are equal to and given by the appropriate components of the curvature tensor.

The tidal forces at the central singularity are not finite, nor are the components of the curvature tensor. Both go to infinity there.

The tidal forces on an accelerating body are, confusingly, not quite the same as the curvature tensor. So the equivalence between the components of the curvature tensor and the measured tidal forces is strictly true only for a non-acclerating body.

The details get technical, but are a result of Bell's spaceship paradox, where the front and tail of a rigid spaceship have to accelerate at different rates if the spaceship is to remain rigid. If the front and tail accelerated at exactly the same rate, the spaceship would have to stretch (this is like the string breaking between two space-ships that accelrate at the same proper accelration).

The difference between the accelerometer readings at the head and tail of the space-ship could reasonably be interpreted as definiing a sort of tidal force. But there is no actual curvature of space-time in this scenario, the spaceships are in perfectly flat space-time.

 

[pawprint]

Thank you pervect. I like Bell, and Wheeler too. But I can only read them in English translation (from the math).

 

[PeterDonis]

There is only one (non-mathematical) point from the entire thread that I have not truly grasped. I accept the concept that, as almost infinite energy is required to hover near the event horizon, gravity can be inferred to become infinite at the EH.

"Gravity" in the sense of "the proper acceleration required to hover at a constant radius". But there are other senses of "gravity" that are *not* infinite at the horizon, as several posters have pointed out. Curvature in the sense of the Riemann curvature tensor, for example, or various scalars derived from it, is perfectly finite at the horizon, but becomes infinite at the singularity.

The key thing you appear to be struggling with is that you are trying to find one single "thing" that can be thought of as "gravity". There isn't. "Gravity" encompasses multiple phenomena, and they don't all "go together" the way one's intuition thinks they ought to. But our intuition is based on a very narrow set of conditions where speeds are small and all aspects of "gravity" are very weak, so they all kind of "look the same". GR has to handle a much wider range of cases, where "gravity" gets a lot stronger and the various phenomena associated with it start acting differently (like proper acceleration vs. curvature at the black hole's horizon).

My problem may simply be due to the impossibility of representing spacetime in three dimensions.

This is a problem, yes, but I would put it slightly differently. I think you are having problems because you are trying to deduce *everything* about gravity from a single diagram. To really get a complete picture, you have to look at multiple representations of the spacetime, each of which picks out a different aspect of it. Then you have to put all the different viewpoints together and understand how they interact. The page I linked to earlier, showing diagrams in Finkelstein, Kruskal, and Penrose coordinates in addition to Schwarzschild coordinates, is an excellent resource for doing that.

My memory is that not many years ago such diagrams of black holes showed an infinitely deep gravity well at the singularity. However now a search reveals the vast majority of such images to resemble that shown here, with almost flat bottoms. Does this represent a paradigm shift or just lazy artists?

Probably lazy artists if they are really intending to show "flat bottoms". But I suspect that what look to you like "flat bottoms" are really infinitely deep wells that just get cut off by the edge of the drawing.

It's worth noting, however, that the "infinitely deep well" idea has problems too. The underlying issue is the temptation to think of the singularity as a "place"--a location "in space". In reality, the singularity is a *spacelike surface*--which means that the closest thing to it in our intuitions is an *instant of time*--a "slice" of the universe (more precisely, of the portion of the universe that's behind the horizon) at a particular time. You can't represent "the universe at an instant of time", or "a portion of the universe at an instant of time" as a spatial point on a spatial diagram. It should really be a *separate* "spatial diagram" all its own.

If you look at the Kruskal or Penrose diagrams on the page I linked to earlier, you will see that they make this obvious: the singularity is a hyperbola that goes from left to right in the Kruskal diagram, and it is a horizontal line in the Penrose diagram. (This is also why we say that the singularity is "in the future", and why it's impossible to avoid the singularity once you're inside the horizon--because you can't avoid moving into the future.)

 

[pawprint]

The key thing you appear to be struggling with is that you are trying to find one single "thing" that can be thought of as "gravity". There isn't. "Gravity" encompasses multiple phenomena, and they don't all "go together" the way one's intuition thinks they ought to. But our intuition is based on a very narrow set of conditions where speeds are small and all aspects of "gravity" are very weak, so they all kind of "look the same". GR has to handle a much wider range of cases, where "gravity" gets a lot stronger and the various phenomena associated with it start acting differently (like proper acceleration vs. curvature at the black hole's horizon)...

...This is a problem, yes, but I would put it slightly differently. I think you are having problems because you are trying to deduce *everything* about gravity from a single diagram.

I first read of time dilation (in science fiction) at the age of 8 or 9 and it took another 12 years before I had intuitively grasped the combined SR implications of mass, time, length and redshift associated with it. I will certainly revisit the Penrose page referred to and spend more time there. GR is stretching my mind, but once it is 'well mixed in' I hope for intuitive understanding.

As an aside I attended a spontaneous lecture by Roger 23 years ago. Everybody was expecting him to talk of matters cosmological but he spoke for 100 minutes on quantum effects in the brain's microtubules! I remember it all the better because it was the first important public event I attended wearing paws rather than shoes.

I missed the multiquote button re pervect's post above, but I smiled when I read of Bell's spaceship paradox.

No, it does not imply that... Further, the enlarged event horizon 'rings' for a while, emitting more GW. These are all oscillations of the metric (or geometry) outside the event horizon.

Can PAllen or somebody else who knows tell me the sort of frequency ranges expected of these 'ringing' waves once they reach flat spacetime? LIGO is said to be unresponsive to frequencies below 200 Hz, but newer instruments are hoped to have much wider bandwidths.

 

[Spin-Analyser]

Pervect's statement about the horizon moving at c past any infaller is simply true. To the infaller it simply appears as the light of prior infallers reaching them. Thus the moment they cross the horizon is the moment they can see all prior infallers. I don't see the tension with any other statements.

Could you clarify this please? Are you saying that an in-faller would see the in-fallers in front of them ( who were of course outside the horizon from a distance ) cross the event horizon as they approach, at which point they disappear from this this observers perspective only to reemerge once the event horizon is reached? This doesn't seem right?

 

[PAllen]

Could you clarify this please? Are you saying that an in-faller would see the in-fallers in front of them ( who were of course outside the horizon from a distance ) cross the event horizon as they approach, at which point they disappear from this this observers perspective only to reemerge once the event horizon is reached? This doesn't seem right?

As long as an infaller is outside the horizon, they see prior infallers as they were closer to the horizon than they are. Note that distances perceived by this infaller are very different from the r coordinate value - there is "lot's of room". Passing the horizon by our chosen infaller is experienced as seeing prior infallers pass the horizon.

There is no disappearance or reappearance.

I came up with an analogy on another thread. Imagine a chain of infalling observers. Imagine a pink flashbulb goes off beyond one end of this chain. Prior to the pink light reaching (say) the last observer in the chain, all prior infallers are seen as before the flash reached them. The moment the flash reaches the last observer is exactly the moment when this observer sees all prior observers flash pink. Thus, the moment the this observer crosses the horizon is the moment they see earlier infallers as of when they crossed the horizon. Factoring light delay, you deduce they all got hit with the flash before you, but you only see them flash pink the same time you do. Similarly, factoring in light delay, this trailing infaller deduces the earlier infallers crossed the horizon before they did.