Black Hole Questions: Mass Increase & Formation

[wywong]

1. From our frame of reference, it takes infinite time for an object to pass the event horizon of a black hole. Does that mean there simply isn't enough time for any black hole to form in the first place?

2. When an object of mass m falls into a black hole of mass M, the mass of the black hole will become M+m, right?

My problem is that the object's mass increases with its speed and approaches infinity near the event horizon. Theoretically its mass can exceed M+m just before it reaches the event horizon, right? To me, that doesn't add up.

Thanks in advance!

Wai Wong

 

[TDS]

A Laymans answers.

Wai,

I hope that you do not mind a Layman's answers to your questions.

1) From our frame of reference the observer should see the object enter the Accresion Disk in a time relative to the observer. Example, an observer sees an object approach the accresion disk at a velocity the would put the object in the accresion disk in a weeks time of being observed. Once the object is trapped in the accresion disk, it now moves at the velocity of the rotation of the disk. At that velocity it may take a year for the object to enter the Event Horizon. The time that it takes for the Star to become a Black Hole would be based on the size of the star and the age of the star. The two situations are not related. In my humble opinion anyway.

2) Logically you are correct. Anytime you add something to something its mass should increase. But I bet that someone here will probably find a way to negate this.

I hope that I have been able to help.

TDS

1. From our frame of reference, it takes infinite time for an object to pass the event horizon of a black hole. Does that mean there simply isn't enough time for any black hole to form in the first place?

2. When an object of mass m falls into a black hole of mass M, the mass of the black hole will become M+m, right?

My problem is that the object's mass increases with its speed and approaches infinity near the event horizon. Theoretically its mass can exceed M+m just before it reaches the event horizon, right? To me, that doesn't add up.

Thanks in advance!

Wai Wong

 

[wywong]

At that velocity it may take a year for the object to enter the Event Horizon.

I think that is not correct. If the object falling into the event horizon is a clock, it will appear to be running slower and slower and almost coming to a standstill just before entering the event horizon. To us, whenever we look at it, we can always see the clock just above the event horizon. Of course, that is purely theoretical, because the photons emitted from the clock would have red-shifted to undetectable energy levels.

Wai Wong

 

[pervect]

1. From our frame of reference, it takes infinite time for an object to pass the event horizon of a black hole. Does that mean there simply isn't enough time for any black hole to form in the first place?

2. When an object of mass m falls into a black hole of mass M, the mass of the black hole will become M+m, right?

My problem is that the object's mass increases with its speed and approaches infinity near the event horizon. Theoretically its mass can exceed M+m just before it reaches the event horizon, right? To me, that doesn't add up.

Thanks in advance!

Wai Wong

Simultaneity is relative. From the point of view of an observer falling into a black hole, there is no problem regarding its existence.

The analogy between the event horizon of a black hole and the so-called Rindler horizon of an accelerating observer helps illustrate the difficulty with the viewpoint that a black hole "doesn't exist" or is a "frozen star". The "frozen star" view used to be quite common, but has more or less faded away. Of course, this is really a philosophical question in disguise, because it is concerned with "existence".

Here's the scoop on the Rindler horizon. If you get into a rocketship, and accelerate at 1 gravity, you can, given a headstart, outrun light. Greg Egan talks a little bit about this at http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

You never exceed the speed of light, but you always stay just a bit ahead of a light beam. As a consequence of this fact, there is an event horizon behind you, which is mathematically quite similar to the event horizon of a black hole. If you think in non-inertial frames, you can say that this event horizon is due to the uniform gravitational field cuased by your acceleration.

Now, suppose you are on such a space-ship. If you keep accelerating constantly, from the POV of the space-ship the Earth never gets beyond a certain critical point, for instance at 1g the Earth never gets much older than 1 year old. So the Earth "freezes" from the POV of the space-ship, and never crosses the horizon. Of course, there is absolutely no problem from the POV of the Earth. Nothing specially happens at 1 year. The problem is entirely with the POV of the spaceship. This suggests caution in adopting the "frozen star" viewpoint, it doesn't always give an accurate picture for all observers. The key point is that the time to fall-in is infinite in the coordinate system of an outside observer, but finite for the coordinate system of an infalling observer.

Onto the second question. The mass of a Schwarzschild black hole increases not by the mass of an object that you drop into it, but by the energy-at-infinity/c^2. (Energy at infinty is the term used by Misner, THorne, Wheeler in "Gravitation"). A more sophisticated way of saying this is that the ADM mass of the black hole and the infalling object is a conserved quantity.

So if you have an object that is motionless at infinity, and let it drop into the black hole, the black hole increases by the mass of that object. If you have an object that is moving rapidly at infinty, the mass of the black hole increases by more than the mass of a black hole. If you have an object that does not have enough energy to espcae to infinity, the mass of the black hole increases by LESS than the mass of the object. It is the energy-at-infinty that is conserved. The conservation of the energy-at-infinty is due to the fact that the Schwarzschild space-time is static. (The ADM formulation of this conservation law relies on the fact that space-time is asymptotically flat, rather than the fact that it's static. The Schwarzschild space-time is both. The ADM formulation is needed if the infalling object is significant compared to the mass of the black hole, as the resulting space-time is no longer Schwarzschild nor static. However, the "energy-at-infinty" formulation is much more tractable mathematically and is the one given in most introductory textbooks.

See the thread on energy conservation in GR for more on that topic.

 

[wywong]

The "frozen star" view used to be quite common, but has more or less faded away. Of course, this is really a philosophical question in disguise, because it is concerned with "existence".

I have no problem about the existence of black holes from the infalling object's POV. My point is, we can never feel the effects of black holes. What we can feel is the effects of stars or other matter 'about' to become black holes, unless we are unlucky to cross the event horizon ourselves. In other words, any attempt to explain any phenomenon using black holes must be flawed because the effects of black holes have not reached us yet. One can only say a certain phenomenon is caused by a dying star about to become a black hole.

Onto the second question. The mass of a Schwarzschild black hole increases not by the mass of an object that you drop into it, but by the energy-at-infinity/c^2. (Energy at infinty is the term used by Misner, THorne, Wheeler in "Gravitation"). A more sophisticated way of saying this is that the ADM mass of the black hole and the infalling object is a conserved quantity.

So if you have an object that is motionless at infinity, and let it drop into the black hole, the black hole increases by the mass of that object.

My problem is that the object's relativistic mass itself exceeds the total mass when it approaches the event horizon. Thus mass cannot be conserved. Such an anomaly can be avoided if my assertion above is correct, i.e. such anomaly has not happened yet.

Wai Wong

 

[wywong]

I have no problem about the existence of black holes from the infalling object's POV.

On second thought, I do have problem about the infalling object's POV. My question is: can the infalling object feel the gravity of the BH? It seems to me that the answer should be no, because light just above the horizon has not reached the object, and gravity cannot travel faster than light! Instead, it should be feeling the gravity of the BF forming matter before the BH is formed.

From the object's POV, it should always see a lot of matter above the event horizon about to enter the BH. The closer it gets to the event horizon, the more photons will hit it. Before it can cross the event horizon, it will be disintegrated by the radiation and extreme temperature.

I am likely to be wrong, but can anyone enlighten me?

Wai Wong

 

[MeJennifer]

On second thought, I do have problem about the infalling object's POV. My question is: can the infalling object feel the gravity of the BH? It seems to me that the answer should be no, because light just above the horizon has not reached the object, and gravity cannot travel faster than light! Instead, it should be feeling the gravity of the BF forming matter before the BH is formed.

By Einstein's equivalence principle a free falling point mass never feels the influence of gravity.
However since the gravitational field of a black hole is not uniform there are tidal effects, so if the object is of any significant size it would deform.

 

[wywong]

By Einstein's equivalence principle a free falling point mass never feels the influence of gravity.
However since the gravitational field of a black hole is not uniform there are tidal effects, so if the object is of any significant size it would deform.

I agree that the object will experience tidal effects, but the gravity it experiences does not come from the black hole, it was released from the raw materials that formed the black hole *before* they cross the event horizon.

As a thought experiment, suppose a black hole was formed 10 billion years ago and a clock set at 0:00 was dropped 1m above the event horizon into the black hole. When we observe the clock now, we can still see a very thin clock at time 0.0...01s about to cross the event horizon. It is time dilation that turn this 0.0...01s into our time of 10 billion years. 20 billion years from now, our descendants can still see the clock, just a tiny bit closer to the event horizon. In other words, it takes 20 billion years for light to travel that tiny distance. Since gravity has the same speed as light, it takes gravity the same 20 billion years to travel that tiny distance. As the black hole is only 10 billion years old, its gravity has not traversed even that tiny distance! The gravity that reaches us come from objects that were outside the event horizon like the clock.

Again, my assertion is that we can never feel the effect of black holes.

Wai Wong

 

[MeJennifer]

IAs a thought experiment, suppose a black hole was formed 10 billion years ago and a clock set at 0:00 was dropped 1m above the event horizon into the black hole. When we observe the clock now, we can still see a very thin clock at time 0.0...01s about to cross the event horizon. It is time dilation that turn this 0.0...01s into our time of 10 billion years. 20 billion years from now, our descendants can still see the clock, just a tiny bit closer to the event horizon. In other words, it takes 20 billion years for light to travel that tiny distance. Since gravity has the same speed as light, it takes gravity the same 20 billion years to travel that tiny distance. As the black hole is only 10 billion years old, its gravity has not traversed even that tiny distance! The gravity that reaches us come from objects that were outside the event horizon like the clock.

Again, my assertion is that we can never feel the effect of black holes.

Actually you are mistaken.
You thought experiment assumes that the mass making up the black hole was created instantly. Instead it was simply caused by the accumulation of enough mass and an insufficient resistance from EM and other forces to counter the gravitational collapse. Each time an additional mass object joined the sphere it adjusted the spacetime curvature was adjusted.

Think of the whole spacetime manifold of the universe, every particle's shape of the worldline is subject to the local curvature of spacetime. But at the same time each particle with mass or anything with energy will change the curvature of spacetime.
Now in GR there is no action at a distance. An object removed far away from a black hole starts to move in the direction of the black hole because the local curvature guides it not because there is some information on the distant mass density.

 

[Thrice]

1. From our frame of reference, it takes infinite time for an object to pass the event horizon of a black hole. Does that mean there simply isn't enough time for any black hole to form in the first place?

That comes from a bad choice of coordinates. The object goes through the horizon in finite proper time. If you want to describe the event using Schw. coordinate time, you'll find that the object goes through infinite coordinate time in order to reach the event horizon, and then goes back through (coordinate) time until reaching the interior in a net coordinate time that is not too different from the proper time.

2. When an object of mass m falls into a black hole of mass M, the mass of the black hole will become M+m, right?

Sure.

My problem is that the object's mass increases with its speed and approaches infinity near the event horizon. Theoretically its mass can exceed M+m just before it reaches the event horizon, right? To me, that doesn't add up.

Mass doesn't increase, really. We've tried to get that interpretation out of relativity for some time now.

 

[pervect]

On second thought, I do have problem about the infalling object's POV. My question is: can the infalling object feel the gravity of the BH? It seems to me that the answer should be no, because light just above the horizon has not reached the object, and gravity cannot travel faster than light! Instead, it should be feeling the gravity of the BF forming matter before the BH is formed.

From the object's POV, it should always see a lot of matter above the event horizon about to enter the BH. The closer it gets to the event horizon, the more photons will hit it. Before it can cross the event horizon, it will be disintegrated by the radiation and extreme temperature.

I am likely to be wrong, but can anyone enlighten me?

Wai Wong

See for instance
http://casa.colorado.edu/~ajsh/collapse.html#collapse

Image of the collapsed sphere

Sphere after collapse.

Even though the sphere has collapsed to a point from its own point of view, an outside observer (like us) sees the sphere appear to freeze at its horizon, becoming more and more redshifted, and fainter and fainter.

The images of layers at different levels appear to merge together into a single surface, the horizon.

As time goes by, images of layers from close to the centre of the sphere expand and also merge with the images of the outer layers (the movie above doesn't show this, because it was too confusing to include more than two layers; but the movie below does illustrate how images of inner layers expand and merge with outer layers). The merging of images of inner layers never quite includes the central point itself, which still appears (highly redshifted) as a point at the centre of the sphere.

Answer to the quiz question 9:

From the point of view of an outside observer, a star collapsing to a black hole never appears to collapse, but rather freezes at the horizon. How then can it be said that the star collapses to a singularity, if it never appears to collapse even till the end of the Universe?

The star does in fact collapse inside the horizon, even though an outside observer sees the star freeze at the horizon. The freezing can be regarded as a light travel time effect. As described here, space can be regarded as falling into the black hole, reaching the speed of light at the horizon, and exceeding the speed of light inside the horizon. Thus photons that are exactly at the horizon and pointed vertically upwards hang there for ever, their outward motion through space at the speed of light being canceled by the inward flow of space at the speed of light. It follows that it takes an infinite time for light to travel from the horizon to the outside world. The star does actually collapse: it just takes an infinite time for the information that it has collapsed to get to the outside world.

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

Won't it take forever for you to fall in? Won't it take forever for the black hole to even form?

Not in any useful sense. The time I experience before I hit the event horizon, and even until I hit the singularity-- the "proper time" calculated by using Schwarzschild's metric on my worldline-- is finite. The same goes for the collapsing star; if I somehow stood on the surface of the star as it became a black hole, I would experience the star's demise in a finite time.

On my worldline as I fall into the black hole, it turns out that the Schwarzschild coordinate called t goes to infinity when I go through the event horizon. That doesn't correspond to anyone's proper time, though; it's just a coordinate called t. In fact, inside the event horizon, t is actually a spatial direction, and the future corresponds instead to decreasing r. It's only outside the black hole that t even points in a direction of increasing time. In any case, this doesn't indicate that I take forever to fall in, since the proper time involved is actually finite.

At large distances t does approach the proper time of someone who is at rest with respect to the black hole. But there isn't any non-arbitrary sense in which you can call t at smaller r values "the proper time of a distant observer," since in general relativity there is no coordinate-independent way to say that two distant events are happening "at the same time."

I believe this question is also addressed in Kip Thorne's book (Black Holes: Einstein's outgrageous legacy) but my copy has wandered off again.

Note that the question of how the gravity gets out of the black hole has also been addressed in the above two web pages, though there is perhaps slightly less agreement about how to explain the answer. But the answer is very clear - gravity does get out of a black hole, and so does the columb force due to the black hole's charge.

You might also want to look at
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html"
http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html"

 

[wywong]

That comes from a bad choice of coordinates. The object goes through the horizon in finite proper time. If you want to describe the event using Schw. coordinate time, you'll find that the object goes through infinite coordinate time in order to reach the event horizon, and then goes back through (coordinate) time until reaching the interior in a net coordinate time that is not too different from the proper time.

Thanks for your reply!

Pardon me for still using the cordinate time. If the object can go back through coordinate time, does that mean it can exist in two places (one outside and one inside the event horizon) at the same coordinate time? If so, can we feel the gravity of the object (and all other stuff) inside the event horizon?

Mass doesn't increase, really. We've tried to get that interpretation out of relativity for some time now.

How about energy? At some point before the event horizon, the kinetic energy of that object will exceed (m+M)c^2, which is impossible. So, the object can never reach that point, but yet it can somehow 'tunnel' through that barrier into the black hole!? Is it possible to calculate the coordinate time when such tunnelling occurs?

Wai Wong

 

[pervect]

Thanks for your reply!How about energy? At some point before the event horizon, the kinetic energy of that object will exceed (m+M)c^2, which is impossible. So, the object can never reach that point, but yet it can somehow 'tunnel' through that barrier into the black hole!? Is it possible to calculate the coordinate time when such tunnelling occurs?

Wai Wong

You are using SR formulas here where you need to be using GR formulas. The correct formula for the "energy at infinity" of an infalling object is a constant. You can find the correct formulas in several textooks, or online at http://www.fourmilab.ch/gravitation/orbits/ where the 'energy at infinity' is called ~E.

Furhtermore, when the infalling object crosses the event horizon, what gets added to the black hole's mass is the "energy at infinity" / c^2, assuming that the infalling object has a negligible mass compared to that of the black hole so that the momentum of the black hole is essentially unchanged. The mass of the infalling object does not get added - what adds is the energies. For instance, an object of rest mass m, suspended just above the event horizon, and dropped in will not contribute appreciably to the mass of the black hole, because its "energy at infinity" will be essentially zero.

 

[Thrice]

Pardon me for still using the cordinate time. If the object can go back through coordinate time, does that mean it can exist in two places (one outside and one inside the event horizon) at the same coordinate time? If so, can we feel the gravity of the object (and all other stuff) inside the event horizon?

Yeah the event horizon does increase in finite coordinate time so yes you will need more than one worldline with these coordinates. But we're fine so long as the particle is out of reach by the time you register the increase. IE even a photon can't catch up to it now ("before it crosses over"). See this is just strange coordinates.

 

[wywong]

Actually you are mistaken.
You thought experiment assumes that the mass making up the black hole was created instantly. Instead it was simply caused by the accumulation of enough mass and an insufficient resistance from EM and other forces to counter the gravitational collapse. Each time an additional mass object joined the sphere it adjusted the spacetime curvature was adjusted.

I did not assume the black hole was formed instantly. I just assume the black hole was there when the clock was dropped 10 billion years ago. To me and my descendants, the clock is always outside the event horizon. In other words, nothing has ever joined the sphere. Regardless of when the black hole was formed, its gravity has not travesed the tiny distance that the clock takes 20 billion years to traversed.

Think of the whole spacetime manifold of the universe, every particle's shape of the worldline is subject to the local curvature of spacetime. But at the same time each particle with mass or anything with energy will change the curvature of spacetime.
Now in GR there is no action at a distance. An object removed far away from a black hole starts to move in the direction of the black hole because the local curvature guides it not because there is some information on the distant mass density.

My point is there is curvature of spacetime around a 'black hole', but that curvature is caused by the black hole's building materials before they cross the event horizon. You can't count the gravity of the materials twice. You can only ignore the infalling materials' gravity only if they have crossed the event horizon.

Wai Wong

 

[MeJennifer]

I did not assume the black hole was formed instantly.

I realize that, but that is the whole problem with your thought experiment.

I just assume the black hole was there when the clock was dropped 10 billion years ago. To me and my descendants, the clock is always outside the event horizon.

Correct.

In other words, nothing has ever joined the sphere.

Here you are obviously wrong. It actually happened, it did pass the event horizon but you simply cannot detect it from your frame of reference.

Regardless of when the black hole was formed, its gravity has not traversed the tiny distance that the clock takes 20 billion years to traversed.

Again you are assuming that because you do not see it going past the event horizon that it did not happen. It did happen, but you simply cannot detect it.

A black hole's event horizon is not the only type of event horizon in relativity. For instance, two objects that are accelerating away from each other with a given initial distance cannot see each other's light signals either. Would you by analogy conclude that nothing is happening at the other location or perhaps even that it does not exists?

 

[wywong]

Thanks to the responses from you experts, but I am unable to comprehend most of your arguments and links, except for those based on frozen star theory which I agree.

Let me perform a final thought experiment. Suppose I dive into a nearby black hole today wearing a mirror on my back. A billion years from now, someone, say Alice, on Earth sends me a flash of light. My questions are:

a. Will I receive the flash before I cross the event horizon? I think so.
b. Will the flash be blueshifted or redshifted? I think it is extremely blueshifted.
c. Will the reflection of the flash be received by earthlings some time later? I think the reflection will be received several billion years from now somewhat redshifted.
d. If the flash contains information (e.g. Morse code representation of Alice), is the information intact in the reflection? I think so.
e. If I decide to return after receiving the flash, will it be too late? I don't think so. I think I can return to the Earth to meet Alice's descendants.

Am I correct? If so, then the frozen star scenario is not an optical illusion - I can still send information 1 billion Earth years after I dive in, and Alice's persuasion can rescue me from falling into a black hole 1 billion years after I dive!

Wai Wong

 

[pervect]

Thanks to the responses from you experts, but I am unable to comprehend most of your arguments and links, except for those based on frozen star theory which I agree.

Let me perform a final thought experiment. Suppose I dive into a nearby black hole today wearing a mirror on my back. A billion years from now, someone, say Alice, on Earth sends me a flash of light. My questions are:

a. Will I receive the flash before I cross the event horizon? I think so.

You will not receive the flash of light before you cross the event horizon. This is mentioned in several of the FAQ's I've been quoting.

For example http://casa.colorado.edu/~ajsh/singularity.html

Answer to the quiz question 5: False. You do NOT see all the future history of the world played out. Once inside the horizon, you are doomed to hit the singularity in a finite time, and you witness only a finite (in practice rather short) time pass in the outside Universe.

and also http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

Will you see the universe end?
If an external observer sees me slow down asymptotically as I fall, it might seem reasonable that I'd see the universe speed up asymptotically -- that I'd see the universe end in a spectacular flash as I went through the horizon. This isn't the case, though. What an external observer sees depends on what light does after I emit it. What I see, however, depends on what light does before it gets to me. And there's no way that light from future events far away can get to me. Faraway events in the arbitrarily distant future never end up on my "past light-cone," the surface made of light rays that get to me at a given time.

That, at least, is the story for an uncharged, nonrotating black hole.

If you have the math, you can work this out from a standard Finklestein diagram. I'm sorry if you don't have the background to understand the arguments, I'm not quite sure what to do about that. I could probably dig up some textbook references in addition to the online web references I've been quoting, but I suspect that's not the issue here.

Have you actually been reading any of the web references I've been posting on this fascinating subject, or have you just been making stuff up out of your own imagination? I get the unfortunate impression you've been mostly "making stuff up" rather than doing any serious reading (including the popular references I've quoted which should be accessible enough to show you, at a minimum, that your ideas are not correct, even if you don't have the math at the current time to go into more details.)

b. Will the flash be blueshifted or redshifted? I think it is extremely blueshifted.

I've worked out what happens in the specific case of someone free-falling into a black hole from infinity (i.e. zero energy at infinity) and viewing a radial light beam from behind him. The light that that particular observer sees is redshifted by a factor of 2:1 when he is at the event horizon. Detailed calculations are required, because gravity blue-shifts the light, while the doppler effect redshifts the light. Another poster here has confirmed that answer. The general answer will depend on one's exact trajectory - one can see the distant light either redshifted or blueshifted, depending on the exact details. The red or blueshift will also depend on the angle, the case I worked out was the simple case where one looks directly astern.

http://casa.colorado.edu/~ajsh/, which has some movies of what someone would see falling into a Schwarzschild black hole, also talks a bit about this in more detail (redshift/blueshift vs angle).

many of the remainig points and questions are somewhat irrelevant given the above.

 

[wywong]

Here you are obviously wrong. It actually happened, it did pass the event horizon but you simply cannot detect it from your frame of reference.

As far as I understand, the two events - the clock crossing the event horizon, and we see the frozen clock now - are spacelike. So I don't understand why you use past tense for the former event. I think the order of such event pair depends on which observer you are talking about. For us, the former event should be in the future.

Again you are assuming that because you do not see it going past the event horizon that it did not happen. It did happen, but you simply cannot detect it.

When did it happen? According to the clock's proper time, it takes a finite time (say 1ns) for it to reach the event horizon. Does that mean the clock crossed the event horizon 10 billions years minus 1ns ago? Of course not. The 1ns dilates to infinity in our coordinate time.

A black hole's event horizon is not the only type of event horizon in relativity. For instance, two objects that are accelerating away from each other with a given initial distance cannot see each other's light signals either. Would you by analogy conclude that nothing is happening at the other location or perhaps even that it does not exists?

Firstly the situation is different because there is no time dilation caused by gravity.

Secondly, if the objects are allowed to stop acceleration, they can find out if the other object exists. But if there is a physical law that prohibit them from accelerating, and no third observer can be present, then the answer to your question is purely philosophical. Hypotheses that say there are 0, 1 or 2 objects at the other end are equally unprovable.

According to the following http://casa.colorado.edu/~ajsh/collapse.html" :

Gravity does not escape from a black hole. Gravity moves at the speed of light, and cannot get from inside the horizon to the outside world. The gravity felt by a person outside a black hole is the gravity of the stuff that fell long ago into the black hole.

So whether the black hole is formed in the past or in the future makes no practical difference.

On the other hand, if one uses a black hole for any calcuation, the result is just an approximation of the remnant effect of the collapsing star.

Wai Wong

 

[wywong]

You will not receive the flash of light before you cross the event horizon. This is mentioned in several of the FAQ's I've been quoting.

For example http://casa.colorado.edu/~ajsh/singularity.html

and also http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

Both links say I won't see the future and that is what I couldn't comprehend. My rationale was: I am catching up with future, so whatever future event it is, it is a past event to me before I cross the event horizon. So their use of the term 'future' didn't make sense to me. Of course I was mistaken. From the POV of Alice, although I am not yet cross the horizon, her flash cannot catch up with me because I am accelerating away. From my POV Alice is still future when I cross the event horizon.

But that doesn't mean I can't see future events like Alice's flash. Before I reach the singularity, I might see her flash. See

http://www.engr.mun.ca/~ggeorge/astron/blackholes.html"

The fall through the event horizon is survivable, but the fall through the Cauchy horizon is not. All the light which will ever fall on the black hole in the entire future of the Universe will catch up with the observer before he crosses the Cauchy horizon. Looking up out of the hole he will view the entire, possibly infinitely long, history of the Universe from light whose blueshift and energy increase without limit, all in a matter of seconds. The energy falling on the observer at the instant of crossing the Cauchy horizon will be infinite.

That is somewhat like what I envisaged in my thought experiment but is contrary to either of the above links. To me, what is perceived beyond the event horizon is anybody's guess, because no one knows how our senses work when time and space swap, and even whether GR works there.

If you have the math, you can work this out from a standard Finklestein diagram. I'm sorry if you don't have the background to understand the arguments, I'm not quite sure what to do about that. I could probably dig up some textbook references in addition to the online web references I've been quoting, but I suspect that's not the issue here.

Imagine teaching a child about the concept of negative numbers. He will always come up with questions, some silly, some sensible before he grasps it. The way to teach him is by answering his questions and give analogies. That is why I asked here. Luckily I got it (I think) after your answers to my final thought experiment. I am really grateful for your help, honestly. I must also acknowledge other experts' responses are helpful and appreciated.

Have you actually been reading any of the web references I've been posting on this fascinating subject, or have you just been making stuff up out of your own imagination?

The answer to both questions is yes. I even had read Kip Thorne's Black Hole book which thankfully doesn't contain many equations. And of course I made stuff up except for the energy question which I read from Scientific American. If I have seen a reference that explains *exactly* my questions, then I wouldn't have asked those silly questions here. The problem is you see certain pages have already answered my questions but I don't see how they translates to my case.

I get the unfortunate impression you've been mostly "making stuff up" rather than doing any serious reading (including the popular references I've quoted which should be accessible enough to show you, at a minimum, that your ideas are not correct, even if you don't have the math at the current time to go into more details.)

My final thought experiment is flawed, but I still think my other questions are legitimate. Most of the references I read are based on the infalling object's POV. What I am interested in is a safe observer's POV. I don't think it is incorrect to say the black hole has not formed. From my understanding, time dilation is not an illusion; it is reality. Black holes have not formed is not an illusion; it is reality. I am not saying theories that say black holes exist are incorrect. They are just different interpretations of reality. Interpretations that lead to exactly the same predictions are equally good and is a matter of choice. A theory that leads to exactly the same predictions as others in some situations and does not apply to other situations can be said to be not as robust but can't be said to be incorrect.

While the existence of black holes is debatable, its effect is real and has to be explained. From the link you gave me http://casa.colorado.edu/~ajsh/collapse.html#collapse"

Gravity does not escape from a black hole. Gravity moves at the speed of light, and cannot get from inside the horizon to the outside world. The gravity felt by a person outside a black hole is the gravity of the stuff that fell long ago into the black hole.


That is consistent with the frozen star theory which I can comprehend. I dare say strictly speaking the frozen star theory and black hole theory do not exactly give the same predictions, and the frozen star theory is more precise (I made this up, again)! For example, if a massive object fell into a nearby 'black hole' a billion years ago, the frozen star theory should predict slight asymmetry in gravity or spacetime curvature even now, wheras a black hole is symmetrical. As an analogy, a beaker of hot liquid left at room temperature can be assumed to reach room temperature after a few hours or days, but that is just an approximation - it never quite reaches room temperature (assuming the simple thermodynamic equations).

To me, black holes are like Newton's laws, useful because they are simple enough, but they are just approximations. Just like Newton's laws, there are situations like accretion where the Black Hole theory is inadequate and the frozen star paradigm is needed (I didn't make this up). Also it is obvious to me how information is preserved in a frozen star while even the great minds find it hard to tell whether information is lost in a black hole.

I may be like a primary school student who is satisfied with a planetary model of an atom, but as long as it satisfies me, I am content.

Thanks very much!

Wai Wong

 

[George Jones]

That is somewhat like what I envisaged in my thought experiment but is contrary to either of the above links.

Hmmm, from

http://math.ucr.edu/home/baez/physic...s/fall_in.html

That, at least, is the story for an uncharged, nonrotating black hole. For charged or rotating holes, the story is different. Such holes can contain, in the idealized solutions, "timelike wormholes" which serve as gateways to otherwise disconnected regions-- effectively, different universes. Instead of hitting the singularity, I can go through the wormhole. But at the entrance to the wormhole, which acts as a kind of inner event horizon, an infinite speed-up effect actually does occur. If I fall into the wormhole I see the entire history of the universe outside play itself out to the end. Even worse, as the picture speeds up the light gets blueshifted and more energetic, so that as I pass into the wormhole an "infinite blueshift" happens which fries me with hard radiation. There is apparently good reason to believe that the infinite blueshift would imperil the wormhole itself, replacing it with a singularity no less pernicious than the one I've managed to miss. In any case it would render wormhole travel an undertaking of questionable practicality.

This looks very similar to the passage (for rotating black holes) that you quoted.

To me, what is perceived beyond the event horizon is anybody's guess, because no one knows how our senses work when time and space swap, and even whether GR works there.

For a large, ideal non-rotationg black hole, which is a valid solution to the equations of GR, both our senses and GR work fine within the horizon. In particular, time and space don't "swap" inside the horizon. What does happen is that: a poor choice of labels is used; spacetime becomes non-stationary.

Here is an analogy. In some city, imagine that you are driving East on Bridge Street East. After the street makes a sharp left, you are driving almost north on Bridge Street East. East and North did not interchange, it is just that the labellng system has become poor.

In the same manner as street names are convenient labels that humans assign to positions in cities, spacetime coordinates (like r) are just labels assigned by humans to spacetime events. Inside the event horizon, r is a timelike coordinate, so it would make more sense to chanlge the name of the human-assigned label r to something more descriptive. For (partially) historical reasons, this isn't done.

Similarly, in the above city, after the left, it would make sense to change the human-assigned label Bridge Street East to something like Bridge Street North. This hasn't been (and won't be) done, because the city's inhabitants have been calling it Bridge Street East since before anyone can remember.

I describe the non-stationary aspect of spacetime (as well as the switch of labels) as

This is reason that, inside the event horizon, t is a space coordinate and r is a time coordinate. Their names are very misleading, but the metric tells all. Since we must alway move forward in time, and r labels time inside the horizon, hitting the r = 0 singularity is inevitable.

in post#22 in https://www.physicsforums.com/showthread.php?p=929751#post929751" You might want to scan this thread, leaving out the math.

 

[wywong]

Thanks George.

For a large, ideal non-rotationg black hole, which is a valid solution to the equations of GR, both our senses and GR work fine within the horizon.

For our senses to work, electricity and chemicals must flow to and fro various parts of the nervous system, and they are slower than c. From your calculation, it already takes light inifinite time to travel to and fro the mirror at the event horizon, can our nervous system really work inside it? Do the magnitudes of current and potential difference across neurons remain unaffected?

I understand GR is still consistent within the event horizon. What I mean is it is unprovable beyond the event horizon. My philosophy is that if a theory cannot make testable predictions, it is no longer a scientific theory.

Regards

Wai Wong

 

[pervect]

Both links say I won't see the future and that is what I couldn't comprehend. My rationale was: I am catching up with future, so whatever future event it is, it is a past event to me before I cross the event horizon. So their use of the term 'future' didn't make sense to me. Of course I was mistaken. From the POV of Alice, although I am not yet cross the horizon, her flash cannot catch up with me because I am accelerating away. From my POV Alice is still future when I cross the event horizon.

But that doesn't mean I can't see future events like Alice's flash. Before I reach the singularity, I might see her flash. See

http://www.engr.mun.ca/~ggeorge/astron/blackholes.html"

The fall through the event horizon is survivable, but the fall through the Cauchy horizon is not. All the light which will ever fall on the black hole in the entire future of the Universe will catch up with the observer before he crosses the Cauchy horizon. Looking up out of the hole he will view the entire, possibly infinitely long, history of the Universe from light whose blueshift and energy increase without limit, all in a matter of seconds. The energy falling on the observer at the instant of crossing the Cauchy horizon will be infinite.

That is somewhat like what I envisaged in my thought experiment but is contrary to either of the above links.

[/quote]

This is a case where you have to really read the find print. You will note if you read carefully that the author is not talking about the standard event horizon, but the inner horizon (also known as the Cauchy horizon) of a rotating balck hole (and not a non-rotating black hole). Note that this also gets talked about in one of the FAQ's, right after the section I snipped, in the section about rotating black holes. So there isn't any real inconsistency in the references.

This is an interesting issue in its own right, which I'll talk about a bit more later. At the moment, I want to point out that it doesn't have anything to do with the simpler issue that we started out discussing, the issue of falling through the event horizon of a non-rotating black hole, or even the issue of falling through the outer (NOT the inner or Cauchy) horizon of a rotating black hole.

In both of these cases (falling through the event horizon of a non-rotating black hole, or through the outer event horizon of a rotating black hole) there is no infinite blue shift, and one does not see the entire history of the universe play out. One will not be "flash fried" as one travels through the event horizon.

Probably the easiest way to explain why your intuition about this case is wrong is to point out that the infalling observer is moving near the speed of light. A crude (and non-rigorous) way of describing the situation is that one has infinite gravitational blue-shift, which is counteracted by an opposite infinite red shift due to one's infalling velocity. The actual result is not really defined by this crude argument, but a more careful analysis shows that an observer falling through a black hole observers experiences only finite redshifts or blueshifts, the exact value of which depends on his trajectory (and the direction in which he looks). This is basically yet another case where the singularity of the Schwarzschild coordinate system obscures the physics.

I'll now digress a bit and talk about the case you raised, the interesting case of the inner horizon of the rotating black hole.

The analysis you posted quotes from, while widespread, is somewhat idealized, for the Cauchy horizon is probably not actually stable. What destablizes the inner horizon of a rotating black hole is is the infalling radiation, which gets blueshifted to infinite energy. The perturbing effects of this energy were not included in the analysis, which means that this analysis, will fairly widely reported, is not very good, because it is ignoring effects of infinite magnitude.

Because of this instability, the exact inner structure of rotating black holes is currently under some debate.

The best reference I'm aware of for the actual geometry of a rotating black hole is http://arxiv.org/abs/gr-qc/9902008. The shortest summary of the result is that this case is still under investigation. I do not fully understand the "mass inflation" singularity that the authors talk about as being likely (but not yet proven) to exist inside a rotating black hole, or its effects on an infalling observer. I gather that the Penrose and Israel paper http://prola.aps.org/abstract/PRL/v63/i16/p1663_1 is the paper to read to learn more about this issue, but I haven't gotten it from the library yet to study it.

Have you actually been reading any of the web references I've been posting on this fascinating subject, or have you just been making stuff up out of your own imagination?

The answer to both questions is yes. I even had read Kip Thorne's Black Hole book which thankfully doesn't contain many equations.

OK, I'm glad you've been doing some reading, and I'm especially glad that you've read Kip Thorne's excellent book. I'm pretty sure that you'll find that Kip Thorne also comes to the same conclusion that I and the references I've quoted have come to as far as falling through the outer event horizon.

My final thought experiment is flawed, but I still think my other questions are legitimate. Most of the references I read are based on the infalling object's POV. What I am interested in is a safe observer's POV.

The short answer is that simultaneity is relative. I don't find it useful to say that "existence is relative" personally, so the "frozen star" model does not appeal to me. Furthermore, I find that it (the frozen star model) confuses people on issues such as the points that you've raised, such as the fact that one does not see the entire history of the universe when falling through the (outer) event horizon.

To make the question of the "frozen star" vs "already collapsed" model, one would have to come up with a thought experiment where the two models actually differed.

We've already been through one thought experiment, which basically supports the "non-frozen" star model, though I suppose a re-wording of the "frozen star" model could still save it.

Note that if no difference between the two models can be found, the issue becomes one of personal preference and philosophy, rather than science.

 

[wywong]

Thanks for your detail explanations, but I have to admit that I have bitten off more than I can chew. Black hole problems have given me insomnia lately. I may need some time to brush up my math.

To make the question of the "frozen star" vs "already collapsed" model, one would have to come up with a thought experiment where the two models actually differed.

I have posted a thought experiment in a new thread https://www.physicsforums.com/showthread.php?t=142812"

I have the hunch that, since black hole derviations do not take into account of strong force, the differential equations used are only approximation. Although the strong force is undetectable outside the nucleus, it may still be non-zero. That may cause the coordinate time for light to cross the event horizon to be finite, albeit unimaginably high, say a google year. In that case, black hole will not form even in proper coordinate, and what is inside a black hole will become fairy tales.

Wai Wong