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Thoughts on electrically charged black holes...

by mrspeedybob
Tags: black, charged, electrically, holes
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PAllen
#19
Oct5-11, 01:20 PM
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Quote Quote by Passionflower View Post
We can have a hovering body momentarily at the EH but aside from that, we can easily calculate the velocity at the EH between a free falling observer falling at escape velocity and compare those to the velocities of a free falling observer from a given r value and from a free falling observer with an initial velocity at infinity. In both cases we calculate that the velocity is c.
A path even momentarily stationary at the event horizon has a lightlike tangent rather than a timelike tangent. Thus it would represent the frame of light, which is normally considered undefined in relativity.

No material instrument will ever locally measure the velocity of a body to be equal or greater than c. As I have explained, this is mathematically impossible in GR and SR (conventionally interpreted; let's not sidetrack into tachyons or the OPERA measurement).
PAllen
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Oct5-11, 01:28 PM
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Quote Quote by Passionflower View Post

But if you disagree and do not think it is c, I suppose you would not mind telling me the velocity between a free falling observer at escape velocity and an observer dropped at say R=10 at the EH?

We can even continue past the EH, while the spacetime is no longer stationary we could still calculate the local velocity between two observers.
Sure you can continue timelike paths past the event horizon. Sure you can compute relative velocity of two objects passing the horizon at the same event with different infall histories. You will never get c for the relative velocity. To claim you do amounts to the claim that timelike unit vector expressed in some local frame becomes a null vector. This is just mathematically impossible. Whatever you are calculating it cannot be a velocity of material body measured locally by a material instrument.
DrGreg
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Oct5-11, 06:20 PM
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Quote Quote by Passionflower View Post
We can have a hovering body momentarily at the EH...
No you can't.

You've got all this the wrong way round. You cannot locally measure the velocity of anything relative to the event horizon, but you can locally measure the velocity of the event horizon relative to something that is falling through it, and the answer is always c (no matter what height the object was dropped from).

You cannot measure anything relative to the event horizon for exactly the same reason that a photon does not have a frame of reference.
mrspeedybob
#22
Oct18-11, 06:38 PM
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Thank you all for your replies.

I have spent the last 2 weeks contemplating this problem and what you have said. I'll try to walk through my thoughts in a logical way. Let me know if I have it right.

If a laser is shown downward from the roof of a building to the ground the light measured at the ground is slightly blue shifted. There are 2 equally correct ways to interpret this result
1. The light has gained energy as it has fallen into the the gravitational field. Since it's speed is fixed it gains the energy in the form of reduced wavelength
2. There must be a 1 to 1 correspondence between the number of waves emitted from the roof and the number received at the ground. Since the frequency at the ground is higher then 1 second at the ground must be longer then 1 second at the roof. This, I believe, is gravitational time dilation and is a well understood phenomena.

Now lets drop an experimenter (Bob) with a laser into a black hole while we (the other experimenters) remain at a distance. As the Bob falls seconds for him become longer compared to our seconds so we see the frequency of the light get lower and lower. As the laser approaches the event horizon we see the light become radio waves. We see the frequency drop to 1 cycle per second, then 1 cycle per day, then 1 cycle per year, etc.
From Bob's perspective, his laser is still emitting light at the same frequency, but as he looks outward he sees (in very blue-shifted light) the rest of the universe growing old at a rate of millions of years per tic of his watch, then billions, then trillions, all before he reaches the event horizon.

The 1'st take-away from this thought experiment is that from our perspective it makes no sense to talk about what happens inside or even at the event horizon because time there is infinitely dilated so from our perspective nothing happens. Relative to us black holes are frozen in time at the instant of their creation. It would be equally correct to say they are black because light cannot escape the gravity or to say they are black because all processes which might create light have been suspended. There is no singularity because from our perspective time, and the process of stellar collapse, stop the instant the density gets large enough to form an event horizon. Taking this logic 1 step further, no event horizon can form at all because as a star collapses its gravity increases, time dilation becomes more sever, and we on the outside see the process of collapse slow down and the light get redder until the light is undetectable and the surface from which it is emitted appears to be of constant size. In other word, it would become a black hole if time dilation had not infinitely slowed its collapse.

Since no event horizon can form it makes no sense to try to understand what happens at or within one.

Since this conclusion startled me I did some googling to try and find a refutation. I found places that say I'm right, for exactly the reasons I explained, and places that say I'm wrong, with explanations I couldn't understand. What is the mainstream view? If my logic is erroneous, where is the flaw?
Ben Niehoff
#23
Oct18-11, 07:56 PM
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Your view is basically right. However, it is also right to say that the event horizon does form, because we can imagine observers that cross it.

The apparent paradox here really boils down to philosophy of science at this point. Which statement should we take to be "real"? Is there a black hole interior or not? Should we define "real" as "that which we can observe", or should we define "real" as "that which we can, using our theories, predict that someone falling in would observe"? So long as we stay outside the horizon, physics doesn't care one way or another.

I take the philosophical stance that nothing really falls into black holes; it all just collects right outside the event horizon. Many physicists share this view because it jibes with our ideas of black hole entropy and Hawking radiation.

But many physicists also take the other view, that we should take the Schwarzschild geometry as real, and the horizon is a perfectly regular part of the geometry, so infalling objects should simply cross it.

What we observe, watching from the outside, is the same either way.
atyy
#24
Oct18-11, 09:48 PM
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Quote Quote by Ben Niehoff View Post
Your view is basically right. However, it is also right to say that the event horizon does form, because we can imagine observers that cross it.

The apparent paradox here really boils down to philosophy of science at this point. Which statement should we take to be "real"? Is there a black hole interior or not? Should we define "real" as "that which we can observe", or should we define "real" as "that which we can, using our theories, predict that someone falling in would observe"? So long as we stay outside the horizon, physics doesn't care one way or another.

I take the philosophical stance that nothing really falls into black holes; it all just collects right outside the event horizon. Many physicists share this view because it jibes with our ideas of black hole entropy and Hawking radiation.

But many physicists also take the other view, that we should take the Schwarzschild geometry as real, and the horizon is a perfectly regular part of the geometry, so infalling objects should simply cross it.

What we observe, watching from the outside, is the same either way.
Is this equivalent to saying:

Within classical GR, the event horizon does form.

With semi-classical GR, the event horizon does not form.
PAllen
#25
Oct19-11, 08:47 AM
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Quote Quote by mrspeedybob View Post
From Bob's perspective, his laser is still emitting light at the same frequency, but as he looks outward he sees (in very blue-shifted light) the rest of the universe growing old at a rate of millions of years per tic of his watch, then billions, then trillions, all before he reaches the event horizon.
This part isn't quite true. You have two competing rates for Bob - light from outside ever more blue shifted, but EH approaching ever faster. If you look at a Krukal Chart of the geometry, you can easily see that up until the moment of reaching the singularity, only finite external history has passed from Bob's point of view. For some external, stationary, light source, there is a definite last light that reaches Bob, the moment he reaches the singularity, and it is is not light from the infinite future.
PAllen
#26
Oct19-11, 08:59 AM
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Quote Quote by Ben Niehoff View Post

I take the philosophical stance that nothing really falls into black holes; it all just collects right outside the event horizon. Many physicists share this view because it jibes with our ideas of black hole entropy and Hawking radiation.
In your philosophy, what happens to the matter at the center of collapsing body? It can't be frozen at the outside. So, it seems you posit that matter throughout the collapsed body is in some frozen state. What laws of physics apply to the central regions (I know, the presumed 'real' laws are not known yet)? If you assume anything like GR you cannot claim the interior is static, and the singularity theorems force the conclusion that catastrophic collapse occurs.

The big problem I see with frozen at horizon interpretations is that for a super-massive black hole, the internal density is not extreme at all - you could even have complete, normal stars inside the radius of last light, that would be seen to slow down, and then 'disappear' due to resdhift and light trapping (as the collapse proceeds). What physics is applying to what were perfectly normal stars that are now apparently frozen and invisible from the outside?

This type of argument leads me to favor the idea that new physics is unrelated to the event horizon. Instead, while the energy density inside the horizon is within the range of present day theories, normal physics proceeds. Sometime before or at the Planck scale, new physics takes over and suspends the collapse.
mrspeedybob
#27
Oct19-11, 11:27 AM
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Quote Quote by PAllen View Post
This part isn't quite true. You have two competing rates for Bob - light from outside ever more blue shifted, but EH approaching ever faster. If you look at a Krukal Chart of the geometry, you can easily see that up until the moment of reaching the singularity, only finite external history has passed from Bob's point of view. For some external, stationary, light source, there is a definite last light that reaches Bob, the moment he reaches the singularity, and it is is not light from the infinite future.
What's a Krukal Chart? I googled it and only found results for Krusal Chart which doesn't seem to pertain.
PAllen
#28
Oct19-11, 11:36 AM
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Quote Quote by mrspeedybob View Post
What's a Krukal Chart? I googled it and only found results for Krusal Chart which doesn't seem to pertain.
I meant Kruskal chart. It is simply a very convenient set of coordinates for black hole geometry, allowing you to easily draw spacetime diagrams that span the horizon, and see the complete causal relationships. The following wikipedia article is a reasonable introduction:

http://en.wikipedia.org/wiki/Kruskal...es_coordinates

You can try reading the "qualitative features" section if you are afraid of the math.
pheno
#29
Jan24-12, 05:28 AM
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Where does the charge of a (charged) black hole reside?
Holesarecool
#30
Mar14-12, 02:10 PM
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Mrspeedybob, you said:

"Taking this logic 1 step further, no event horizon can form at all because as a star collapses its gravity increases, time dilation becomes more sever, and we on the outside see the process of collapse slow down and the light get redder until the light is undetectable and the surface from which it is emitted appears to be of constant size."

A collapsing star will not increase in mass unless something is falling into it during the collapse, so time dialation will be more or less a constant throughout the collapse. The density will certainly increase, and effects of gravity will increase inside the collapsing areas, as mass will fall past it and start to contribut to the field there. Outside the original radius of the collapsing star, there will be no more than tremors in the gravitational field.

Am I wrong anywhere here?

Either way, very nice though experiment.


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