Questions about black holes and wormholes

[hnn]

Questions about black holes:

Various articles mention that it takes infinite amount of time to observe something pass through the event horizon.

• Does this imply that the redshift observed from afar would carry on forever, that the infalling object would just become dimmer and dimmer, but never disappear?

• If so, where do these infinite amount of photons come from? The infalling object stayed outside of EH for a finite amount of time, the amount of photons reflected from the object must also be finite I would think?

• Why do we not see numerous objects that were swallowed by BH in the past being stuck on the "surface" (EH region) of black holes, is it because they're too dim to see?

Questions about wormholes (assuming they exist):

• Wormhole tunnels have no walls, but wormholes have diameters, what happens if an object inside the tunnel move sideways outside the diameter?

• How do wormholes interact with black holes (e.g. interactions inside EH and near singularity)? Can something cross EH and then go through a wormhole and come out from the other end of the wormhole to escape the black hole?

• Can a black hole exist in a wormhole tunnel? Can a wormhole tunnel run across a black hole, if so, how would the black hole affect the tunnel and the stuff traveling inside the tunnel?

• Can a white hole (assuming they exist) exist in a wormhole tunnel, if so, would it fill up the tunnel and cause the wormhole to explode and disappear?

 

[mfb]

• Does this imply that the redshift observed from afar would carry on forever, that the infalling object would just become dimmer and dimmer, but never disappear?

• If so, where do these infinite amount of photons come from? The infalling object stayed outside of EH for a finite amount of time, the amount of photons reflected from the object must also be finite I would think?

It gets dimmer so fast that you quickly get the last photon and nothing else afterwards.

Wormhole tunnels have no walls, but wormholes have diameters, what happens if an object inside the tunnel move sideways outside the diameter?

The same that happens to you if you move eastwards on the surface on Earth: eventually you end up where you started.

For the ideas to combine multiple objects: The result should behave according to general relativity. The details depend on the way things are combined and how the combined metric looks like. An event horizon, by definition, is final - once you cross it you cannot go out.

 

[Upsilon]

Wormholes would not be "tubes" in a traditional sense. You have probably seen the basic analogy of a wormhome in 2D space: you are trying to get from point A to point B on the sheet of paper, so you fold the paper in the 3rd dimension (which is incomprehensible to beings of that 2D space) to where A and B are the same location. Now just try your best to expand that by 1 dimension; your paper becomes 3D space, the circular points A and B become spheres, and you must fold space-time across some 4th dimension (could be time, could be something else, it's up for debate) to have points A and B meet. Essentially as soon as you cross the "border" of the wormhole, you would already be at your destination; you wouldn't pass through any trippy-looking tunnel or anything like that.

If you have seen the movie Interstellar, I think they do a decent job of explaining this despite being a mainstream blockbuster movie. I especially like their visual representation of a wormhole, I feel that it is a valid possibility:

You can clearly see the sphere representing the wormhole, and you immediately see the space on the other side of it.

 

[|Glitch|]

Questions about black holes:

Various articles mention that it takes infinite amount of time to observe something pass through the event horizon.

That statement would only be true from the object that is passing the event horizon's perspective, since velocity is what effects time. To an outside observer, someone not under the influence of the black hole's gravity (effectively "at rest") there would be no difference in time for an object to pass the event horizon of a black hole. However, from the object's perspective (assuming it has mass), time would begin slowing down the closer the object got to the event horizon because its velocity would be approaching the speed of light. So by the time the object actually reaches the event horizon, time will have effectively stopped from the perspective of the object.

 

[mfb]

No, your own perception of your own time never changes. If you fall into a black hole, you will cross the event horizon in a finite time and you can see this.
Observers outside can never see this moment due to time dilation.

 

[|Glitch|]

Wormholes would not be "tubes" in a traditional sense. You have probably seen the basic analogy of a wormhome in 2D space: you are trying to get from point A to point B on the sheet of paper, so you fold the paper in the 3rd dimension (which is incomprehensible to beings of that 2D space) to where A and B are the same location. Now just try your best to expand that by 1 dimension; your paper becomes 3D space, the circular points A and B become spheres, and you must fold space-time across some 4th dimension (could be time, could be something else, it's up for debate) to have points A and B meet. Essentially as soon as you cross the "border" of the wormhole, you would already be at your destination; you wouldn't pass through any trippy-looking tunnel or anything like that.

If you have seen the movie Interstellar, I think they do a decent job of explaining this despite being a mainstream blockbuster movie. I especially like their visual representation of a wormhole, I feel that it is a valid possibility:

You can clearly see the sphere representing the wormhole, and you immediately see the space on the other side of it.

While I completely agree with the explanation, my chief complaint about the movie was that they placed the worm hole within the solar system. In order to have a black hole, or worm hole, you need a minimum of 3 to 5 solar masses. Placing a 3 to 5 solar mass object right next to the planet Saturn is going to have profound and very disturbing consequences on the entire solar system.

 

[|Glitch|]

No, your own perception of your own time never changes. If you fall into a black hole, you will cross the event horizon in a finite time and you can see this.
Observers outside can never see this moment due to time dilation.

I agree that your perception of your own time never changes. The clock of someone at rest remains constant, and so does the clock of the person that is traveling, from their own perspectives. Time dilation is the result of the person who is traveling, not of the person at rest. Time dilation only comes into effect when observing someone elses clock, not your own. So according to the clock of the person traveling they will will never reach the event horizon because their clock will have effectively stopped due to their velocity. The rest of the universe would have frozen in time, from the traveler's perspective. Whereas, to the outside observer (the person at rest), they would see the traveler increase in speed and then vanish beyond the event horizon once they achieve the speed of light.

 

[mfb]

The lower limit for black holes just applies to their formation as stellar remnants. Artificial black holes or primordial remnants can be much smaller - down to the Planck mass or maybe even smaller. In addition, wormholes are not black holes.

I guess you can hand-wave all that away with the reason the wormhole is there (avoiding spoilers).

Time dilation is the result of the person who is traveling, not of the person at rest.

Those categories do not exist in relativity, as motion is relative.

So according to the clock of the person traveling they will will never reach the event horizon because their clock will have effectively stopped due to their velocity. The rest of the universe would have frozen in time, from the traveler's perspective.

Both statements here would contradict each other, but both are wrong.

Whereas, to the outside observer (the person at rest), they would see the traveler increase in speed and then vanish beyond the event horizon once they achieve the speed of light.

Nothing achieves the speed of light apart from light. For outside observers, the observed velocity slows down due to redshift/time dilation.

 

[|Glitch|]

The lower limit for black holes just applies to their formation as stellar remnants. Artificial black holes or primordial remnants can be much smaller - down to the Planck mass or maybe even smaller. In addition, wormholes are not black holes.

I guess you can hand-wave all that away with the reason the wormhole is there (avoiding spoilers).

Those categories do not exist in relativity, as motion is relative.
Both statements here would contradict each other, but both are wrong.
Nothing achieves the speed of light apart from light. For outside observers, the observed velocity slows down due to redshift/time dilation.

Very true, I was indeed referring to stellar remnants with regard to the minimum size of black holes. Artificially created black holes can be any size, as you say. Worm holes are essentially two black holes, one at either end, with a connected singularity. It would still have to be pretty massive in order to be big enough to allow something the size of a spacecraft to pass the event horizon. A black hole as massive as Jupiter would have an event horizon just 4.4 meters in diameter, and still have a dramatic effect on the objects within the solar system if placed anywhere near Saturn.

 

[Upsilon]

While I completely agree with the explanation, my chief complaint about the movie was that they placed the worm hole within the solar system. In order to have a black hole, or worm hole, you need a minimum of 3 to 5 solar masses. Placing a 3 to 5 solar mass object right next to the planet Saturn is going to have profound and very disturbing consequences on the entire solar system.

Perhaps. That's assuming that black holes and wormholes are similar animals, and they very well could be completely different since nobody has even discovered a wormhole yet, and we know next to nothing about black holes.

However my biggest complaint about the scientific accuracy of the movie was how they scaled up the effect of time dilation by hundreds of thousands of times, but hey, there wouldn't really have been a story without it.

 

[stevebd1]

While I completely agree with the explanation, my chief complaint about the movie was that they placed the worm hole within the solar system. In order to have a black hole, or worm hole, you need a minimum of 3 to 5 solar masses. Placing a 3 to 5 solar mass object right next to the planet Saturn is going to have profound and very disturbing consequences on the entire solar system.

While the whole idea of 'black holes can be wormholes' is debatable, for a black hole to be a two way wormhole it would have to be maximal or super-maximal. This involves the black hole having a great deal of spin or charge. An interesting side effect of this is that gravity becomes zero when the BH is maximal, and repellent when the BH is super-maximal (though it wouldn't technically be a BH any more)-

$$\kappa_\pm=\frac{r_\pm-r_\mp}{2(r_\pm^2+a^2)}$$

where $\kappa_\pm$ is the Killing surface gravity at the outer $(r_+)$ and inner $(r_-)$ event horizon, $r_\pm=M\pm\sqrt(M^2-a^2-Q^2)$ (where normally $a^2+Q^2\leq M^2$ applies for a sub-maximal BH) and $M$ represents mass, $a$ represents spin and $Q$ represents charge.

It also reveals a naked singularity, in the case of a rotating black hole, a ring singularity (it might be said that the throat to the wormhole is at the inner horizon (considered a weak singularity) or at the ring singularity). One of the issues with $\kappa=0$ (or less) is that this would violate the third law in https://www.physicsforums.com/threads/black-hole-thermodynamics.762982/(surface gravity of the BH can never become zero).

About two thirds of the way down on the link below, it shows a regular black hole with spin (a<M), a maximal black hole (a=m) and a super-maximal 'black hole' (a>M)
http://inspirehep.net/record/1351202/plots

Even if $\kappa=0$, the BH/wormhole would have such immense spin and/or charge that this would have an effect on the immediate surrounding. Wormhole metric is slightly different to black hole metric and more often than not, I've heard that wormholes require 'negative' energy in order to remain open and this would take care of the gravity issue.

However my biggest complaint about the scientific accuracy of the movie was how they scaled up the effect of time dilation by hundreds of thousands of times, but hey, there wouldn't really have been a story without it.

You might be interested in this thread

 

[|Glitch|]

While the whole idea of 'black holes can be wormholes' is debatable, for a black hole to be a two way wormhole it would have to be maximal or super-maximal. This involves the black hole having a great deal of spin or charge. An interesting side effect of this is that gravity becomes zero when the BH is maximal, and repellent when the BH is super-maximal (though it wouldn't technically be a BH any more)-

$$\kappa_\pm=\frac{r_\pm-r_\mp}{2(r_\pm^2+a^2)}$$

where $\kappa_\pm$ is the Killing surface gravity at the outer $(r_+)$ and inner $(r_-)$ event horizon, $r_\pm=M\pm\sqrt(M^2-a^2-Q^2)$ (where normally $a^2+Q^2\leq M^2$ applies for a sub-maximal BH) and $M$ represents mass, $a$ represents spin and $Q$ represents charge.

It also reveals a naked singularity, in the case of a rotating black hole, a ring singularity (it might be said that the throat to the wormhole is at the inner horizon (considered a weak singularity) or at the ring singularity). One of the issues with $\kappa=0$ (or less) is that this would violate the third law in https://www.physicsforums.com/threads/black-hole-thermodynamics.762982/(surface gravity of the BH can never become zero).

About two thirds of the way down on the link below, it shows a regular black hole with spin (a<M), a maximal black hole (a=m) and a super-maximal 'black hole' (a>M)
http://inspirehep.net/record/1351202/plots

Even if $\kappa=0$, the BH/wormhole would have such immense spin and/or charge that this would have an effect on the immediate surrounding. Wormhole metric is slightly different to black hole metric and more often than not, I've heard that wormholes require 'negative' energy in order to remain open and this would take care of the gravity issue.
You might be interested in this thread

Thank you for that detailed explanation, and the link. Although, would not the Killing radius of a charged, rotating (Kerr-Newman) black hole coincide with its event horizon?

As mfb correctly pointed out, I was basing my opinion upon stellar remnant black holes and not artificially created black holes, which could have any mass and need not be a charged or rotating (Schwarzschild) black hole.

 

[stevebd1]

Thank you for that detailed explanation, and the link. Although, would not the Killing radius of a charged, rotating (Kerr-Newman) black hole coincide with its event horizon?

The equation shows the Killing surface gravity for both the outer and inner horizon, hence the sub text $\pm$, $\kappa_+$ for the outer horizon $(r_+)$ and $\kappa_-$ for the inner horizon $(r_-)$. The equation reduces to the Killing surface gravity for a static BH when no charge or spin is present, $\kappa=1/4M$. Note when charge and/or spin are present, $\kappa_-$ is negative (i.e. repulsive). As spin and/or charge increase, the coordinate radius for the outer horizon reduces (which in turn reduces $\kappa_+$) and the coordinate radius for the inner horizon increases (which increases $\kappa_-$) until at $a^2+Q^2 = M^2$, the two horizons meet (which is at the coordinate radius of M) and the Killing surface gravity becomes zero.