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Is a black hole interior similar to the universe?


md65536
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If you passed through a BH's event horizon and survived the tidal forces, would the interior seem much like the rest of the universe outside of a BH?

 

- Inside the EH, your future light cone points toward the singularity. This means that in every direction that light can travel, is the singularity. Therefore it appears to be all around you. The singularity looks "as big as" all of space.

 

- Every future light cone very close to the singularity is also pointed toward the singularity, so you can't see it. It looks like blackness at the edge of space, receding from you.

 

Light cones of objects around you also tilt toward the singularity. They all look like they're accelerating toward the singularity???, which is in all directions, so it looks like an inflation of space???

 

 

- When you cross rS, the event horizon is a surface that passes you at the speed of light. As you approach the singularity the EH might recede from you faster than the speed of light (read that somewhere, forget where). Might this also appear as the edge of space, receding from you faster than the speed of light? Could it seem to recede into a point on your negative time axis, like a sort of big bang? (I don't think the big bang and CMBR fits this idea.)

 

- Apparently, if you calculate rS for the estimated mass of the universe, it works out to something close to the size of the observable universe (read that somewhere, forget where). So would the analogy only work (if at all) for BHs that immense? Since BHs are inside the universe and part of their mass, would that imply that if a BH is like a universe, you can only fall into smaller BH universes, until you enter one that kills you or ends with you reaching the singularity, perhaps suffering heat death???

 

 

This might belong in speculations, but is there any sense in thinking of the EH of a black hole as the edge of space in the past, and the singularity as the edge of space in the future (to an observer inside the EH)? And then reversing the argument could we examine our universe as though it is a black hole? Or are there certain detectable differences that would rule this out?

 

 

(Shameless speculation: Could the big bang be like all of time passing in the universe that you leave when you cross the EH, in an instant, though it is not seen immediately but instead looks like CMBR? ohmy.png)

Edited by md65536
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If we assume the singularity is an 'edge' to space-time, ie an edge to a distance-time graph ( y=t and x=d ), then the big bang singularity would be the lower edge of the graph. Spacelike and only in the past.

A black hole singularity may be the left edge of the graph, ie timelike and existing for a long time.

 

Could this account for differences ?

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If we assume the singularity is an 'edge' to space-time, ie an edge to a distance-time graph ( y=t and x=d ), then the big bang singularity would be the lower edge of the graph. Spacelike and only in the past.

A black hole singularity may be the left edge of the graph, ie timelike and existing for a long time.

 

Could this account for differences ?

I don't think it would work, because the left edge of the graph would be a single point in space, existing in an observer's past, present, and future. That time-like vertical line for an outside observer, would become a space-like horizontal line for an observer approaching the singularity. It would be everywhere in space, and only in the (inside observer's) future.

 

If it's an "edge" of spacetime to the inside observer, it would be an end of time. I don't know what that could mean, or with the analogy, what it means to "reach" the singularity and what happens then. If the analogy makes sense, then an observer could never reach the singularity in its own frame of reference. The inside observer would be at rest in its own frame, traveling through time at 1s/s, toward the singularity (the end of time), which is all throughout space.

 

 

Edit: Apparently the time to reach the singularity is finite for a free-falling observer, according to GR. This seems to completely break the analogy.

Edited by md65536
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Don't rotate space-time around the observer as he crosses the event horizon. Rotate the light cone of the observer towards the singularity or edge ( a single point in space ). The time to reach the singularity is still finite, but as he crosses the event horizon and the 'blackness' starts coming up to encompass him, he would see all future time go by in the outside universe.

 

I'm not seeing the problems you mention.

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Don't rotate space-time around the observer as he crosses the event horizon. Rotate the light cone of the observer towards the singularity or edge ( a single point in space ).

But... doesn't that light-cone correspond to the local reference frame of the falling observer? The singularity is at some time in the future in any direction the observer points (at different times in different directions).

 

 

Thanks for the replies... I think I'm speaking from naivety and need to study this a lot more before I'll understand it.

 

 

 

Bleh, despite that last statement: The singularity would be approaching from all directions. It would be more like a shrinking Hubble volume of an accelerating universe, in the analogy. But not really... maybe...

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But... doesn't that light-cone correspond to the local reference frame of the falling observer? The singularity is at some time in the future in any direction the observer points (at different times in different directions).

 

 

Thanks for the replies... I think I'm speaking from naivety and need to study this a lot more before I'll understand it.

 

 

 

Bleh, despite that last statement: The singularity would be approaching from all directions. It would be more like a shrinking Hubble volume of an accelerating universe, in the analogy. But not really... maybe...

The singularity would be in all directions the observer could travel in, but couldn't the observer still receive light and other things from outside the black hole? The black hole cannot accelerate the observer to light speed, so any light coming in behind the observer would eventually catch up to it.

 

That would imply that all future directions poit to the singularity, but past directions not pointing toward the singularity would still be observable.

 

Which is weird to try to imagine.

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The singularity would be in all directions the observer could travel in, but couldn't the observer still receive light and other things from outside the black hole? The black hole cannot accelerate the observer to light speed, so any light coming in behind the observer would eventually catch up to it.

 

That would imply that all future directions poit to the singularity, but past directions not pointing toward the singularity would still be observable.

 

Which is weird to try to imagine.

Yes, it's weird. I've been trying to figure this out and I can't.

 

The EH does pass the falling observer at the speed of light. The observer is at rest in its own frame, and the EH (which is traveling at c according to all observers) travels at the local speed of light when it's local (ie. while passing it).

 

The singularity becomes a "time" in your future. Maybe it's counter-productive to consider it being in certain directions. For example say the singularity is like "next tuesday". You could say "anywhere I look, and any direction I go, I will reach next tuesday", but "next tuesday is in all directions" sounds silly. HOWEVER it does seem that depending on which direction you might try to go inside the EH, or perhaps at different locations you might see, next tuesday can come quicker or slower depending on direction.

 

 

Interpreting light cone diagrams...

eventho2.gif

Source: http://faculty.etsu.edu/gardnerr/planetarium/relat/eventho2.gif

 

It seems from the past light cone at r_S (the event horizon), nothing closer to the singularity is in your past light cone. That seems to imply that anything that crossed the EH before you, cannot be seen in a state after it crossed the EH. I don't know if it would fade away or only be visible in a previous state. I must be reading this wrong???? because if you were following something (or even had your arm out in front of your face), you could not see it cross the EH before you do?

 

It does seem that anything you can see, in any direction, is from events farther than you are from the singularity. That sorta makes sense: The direction of the singularity is "the future" and the every event you can see happened in your past, away from the singularity. But this seems to imply that once you cross the EH, the interior of the black hole can't be seen in any way (not what's in it nor a dark void) because it hasn't happened yet!

 

I'm certain I'm looking at this wrong...

 

 

But I think you're right... it seems that everything you can see, all around you, would come from "behind" you.

Edited by md65536
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Maybe the arrow of time reverses at the EH.

Like turning a sock inside out.

According to which observer? And what are the observable or measurable effects?

 

The singularity becomes a "time" in your future.

...

It does seem that anything you can see, in any direction, is from events farther than you are from the singularity. That sorta makes sense: The direction of the singularity is "the future" and the every event you can see happened in your past, away from the singularity. But this seems to imply that once you cross the EH, the interior of the black hole can't be seen in any way (not what's in it nor a dark void) because it hasn't happened yet!

Now I think this is partly wrong. The singularity wouldn't (ever?) be completely inside your future light cone, but it still is completely outside your past light cone. That means that while you still can't observe any events "closer" to the singularity than you are (ie. not any event that has ever happened inside the EH before you crossed it), it can still exist in spacetime outside of your light cone. Some events near the horizon singularity can be considered to have already happened, but they're beyond a coordinate horizon for you. It's not purely in the future... it still exists but is beyond what you can see.*

 

If I'm interpreting the light cones correctly, the location of the singularity would literally escape your observable universe.

 

This next part goes against what I've been told (ie. that you reach the singularity with finite proper time), but I get the sense that your perceived distance to the singularity would grow immensely. It would escape at faster than c, and meanwhile your observable universe would shrink? Or would it be very distorted, with a horizon that is very near in one direction and far in the opposite???

 

 

* Edit: However, once inside the EH, events near the EH (behind you) are still within your past light cone. So even though you're inside the EH, the black hole could still potentially be visible in some way (as darkness, or as stuff falling into it). You can't see anything ahead of you (which is now like time), but you can still see "behind" you, including stuff from near the EH which you've since passed! I think... you should be able to see anything that has ever fallen into the BH???

 

I've rambled about with several contradictory statements, but it seems like what I'm coming around to is that even when you're "inside" a BH, you still can't see what's farther inside it! There would be some kind of distortion of distances and time, but what you could see of the black hole would essentially be like the outside of the BH!

Edited by md65536
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Your terminology is a little confusing MD65536. When the light cone tips over as it crosses the EH the only possible destination (not time ) in your future is the singularity.

 

And I'm still not clear on the statement about the EH being lightlike, ie moving at c with respect to all observers. This would imply to me anyway, that anything which crosses the EH, whether massive or massless, does so at c, which is impossible.

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Your terminology is a little confusing MD65536. When the light cone tips over as it crosses the EH the only possible destination (not time ) in your future is the singularity.

 

And I'm still not clear on the statement about the EH being lightlike, ie moving at c with respect to all observers. This would imply to me anyway, that anything which crosses the EH, whether massive or massless, does so at c, which is impossible.

Yes, I'm probably thinking about tipped cones the wrong way.

 

The EH is a lightlike surface. It is only locally that the speed of the EH is equal to the local speed of light, and locally the observer is at rest. It's like saying "light travels at c relative to me" but it makes no sense to say "This implies that I travel past photons at the speed of light." Being a lightlike surface, you can't speak of your velocity relative to it in local coordinates (where it is moving at the local speed of light).

 

I think reading this comment: http://www.physicsforums.com/showthread.php?p=4378646#post4378646

and some after it, that made it make sense to me.

Edited by md65536
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Yes, it's weird. I've been trying to figure this out and I can't.

 

The EH does pass the falling observer at the speed of light. The observer is at rest in its own frame, and the EH (which is traveling at c according to all observers) travels at the local speed of light when it's local (ie. while passing it).

 

The singularity becomes a "time" in your future. Maybe it's counter-productive to consider it being in certain directions. For example say the singularity is like "next tuesday". You could say "anywhere I look, and any direction I go, I will reach next tuesday", but "next tuesday is in all directions" sounds silly. HOWEVER it does seem that depending on which direction you might try to go inside the EH, or perhaps at different locations you might see, next tuesday can come quicker or slower depending on direction.

 

 

Interpreting light cone diagrams...

eventho2.gif

Source: http://faculty.etsu.edu/gardnerr/planetarium/relat/eventho2.gif

 

It seems from the past light cone at r_S (the event horizon), nothing closer to the singularity is in your past light cone. That seems to imply that anything that crossed the EH before you, cannot be seen in a state after it crossed the EH. I don't know if it would fade away or only be visible in a previous state. I must be reading this wrong???? because if you were following something (or even had your arm out in front of your face), you could not see it cross the EH before you do?

 

It does seem that anything you can see, in any direction, is from events farther than you are from the singularity. That sorta makes sense: The direction of the singularity is "the future" and the every event you can see happened in your past, away from the singularity. But this seems to imply that once you cross the EH, the interior of the black hole can't be seen in any way (not what's in it nor a dark void) because it hasn't happened yet!

 

I'm certain I'm looking at this wrong...

 

 

But I think you're right... it seems that everything you can see, all around you, would come from "behind" you.

 

I know what you mean.

 

It seems to me that your reasoning would hold if you were static (your distance to the singularity were constant over time)

 

As it is, you fall toward the singularity faster than light falls toward it (if the light is pointed away from the singularity).

 

If you could stand on the event horizon and dip your hand under then you wouldn't be able to see your hand. Likewise, if you could stand static anywhere inside the EH then you wouldn't be able to see any event closer to the singularity than you. But as you fall light leaves your hand and your eyes catch up to the light because light pointed away from the singularity falls less fast than your eyes.

 

If you're trying to observe an event inside the event horizon and it is closer to the singularity than you then you will be closer to the singularity than the event when you eventually see the light from the event, but you can see it.

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I know what you mean.

 

It seems to me that your reasoning would hold if you were static (your distance to the singularity were constant over time)

 

As it is, you fall toward the singularity faster than light falls toward it (if the light is pointed away from the singularity).

 

If you could stand on the event horizon and dip your hand under then you wouldn't be able to see your hand. Likewise, if you could stand static anywhere inside the EH then you wouldn't be able to see any event closer to the singularity than you. But as you fall light leaves your hand and your eyes catch up to the light because light pointed away from the singularity falls less fast than your eyes.

 

If you're trying to observe an event inside the event horizon and it is closer to the singularity than you then you will be closer to the singularity than the event when you eventually see the light from the event, but you can see it.

Would light inside the event horizon be able to point away from the singularity, though?

 

If I see myself traveling toward the singularity at less than the speed of light, and I see light traveling away from me at the speed of light in the opposite direction, then I am seeing light increasing the distance between itself and the singularity. If the distance between the light and the singularity is increasing, it should be able to eventually escape the black hole, which should be impossible.

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Would light inside the event horizon be able to point away from the singularity, though?

 

If I see myself traveling toward the singularity at less than the speed of light, and I see light traveling away from me at the speed of light in the opposite direction, then I am seeing light increasing the distance between itself and the singularity. If the distance between the light and the singularity is increasing, it should be able to eventually escape the black hole, which should be impossible.

 

In flat space, free fall coordinates, spacetime is flowing toward the singularity at the Newtonian escape velocity. At the Horizon space flows at the speed of light (I think Md made reference to that). You can think of it like a river. Let me quote a site:

 

 

Picture space as flowing like a river into the black hole. Imagine light rays, photons, as canoes paddling fiercely in the current. Outside the horizon, photon-canoes paddling upstream can make way against the flow. But inside the horizon, the space river is flowing inward so fast that it beats all canoes, carrying them inevitably towards their ultimate fate, the central singularity.

 

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

 

 

Both the light and the observer are moving along in the current. Light is further down stream and he is paddling as hard as he can against the current, but the water is moving faster than he can paddle and he continues down stream. Catching up to him is the observer who is further up stream, but who is making no effort to paddle against the current. They approach each other and they approach the singularity.

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In flat space, free fall coordinates, spacetime is flowing toward the singularity at the Newtonian escape velocity. At the Horizon space flows at the speed of light (I think Md made reference to that). You can think of it like a river. Let me quote a site:

 

 

 

Both the light and the observer are moving along in the current. Light is further down stream and he is paddling as hard as he can against the current, but the water is moving faster than he can paddle and he continues down stream. Catching up to him is the observer who is further up stream, but who is making no effort to paddle against the current. They approach each other and they approach the singularity.

Let's say that the singularity is a waterfall that the current is flowing toward. The light is in a canoe between you and the waterfall. The light is paddling toward you, so the distance between you and the light narrows as you allow yourself to float freely downstream, but the current is moving faster, so the distance between the light and the waterfall is also narrowing.

 

Wouldn't that mean that you'd see the waterfall approaching you faster than the light canoe? Would light travel at something other than c because of the extreme gravity?

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Let's say that the singularity is a waterfall that the current is flowing toward. The light is in a canoe between you and the waterfall. The light is paddling toward you, so the distance between you and the light narrows as you allow yourself to float freely downstream, but the current is moving faster, so the distance between the light and the waterfall is also narrowing.

 

Wouldn't that mean that you'd see the waterfall approaching you faster than the light canoe?

You would never be able to see the waterfall (light canoes can't travel upstream so one could never get away from the waterfall), but essentially yes. The singularity approaches with greater speed

 

Would light travel at something other than c because of the extreme gravity?

Light always travel c relative to local, flat, freefalling coordinates. The extreme mass of the star is the reason space flows radially so fast. I'll quote that site again...

 

Does the notion that space inside the horizon of a black hole falls faster than the speed of light violate Einstein's law that nothing can move faster than light? No. Einstein's law applies to the velocity of objects moving in spacetime as measured with respect to locally inertial frames. Here it is space itself that is moving.

 

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

 

 

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If you could stand on the event horizon and dip your hand under then you wouldn't be able to see your hand. Likewise, if you could stand static anywhere inside the EH then you wouldn't be able to see any event closer to the singularity than you. But as you fall light leaves your hand and your eyes catch up to the light because light pointed away from the singularity falls less fast than your eyes.

 

I think that length contraction comes into play here.

If you imagine 2 observers falling into a BH together, and just as approaching the EH one accelerates away (assuming it has unlimited energy resources) to remain stationary while the other continues free-falling, then the difference in speeds of the two observers must be near c? So the distances they measure will be severely length contracted. I might be wrong but I think the "stationary" observer will now see the EH as far away, as the length stops being contracted. The EH would again have to appear "frozen" to an observer stationary relative to it? An observer can't hover at the EH, but can it get arbitrarily close? Anyway, no matter how close or far, if you dipped your hand (or a long rope) in, you couldn't possibly get it back!

Would light inside the event horizon be able to point away from the singularity, though?

 

If I see myself traveling toward the singularity at less than the speed of light, and I see light traveling away from me at the speed of light in the opposite direction, then I am seeing light increasing the distance between itself and the singularity. If the distance between the light and the singularity is increasing, it should be able to eventually escape the black hole, which should be impossible.

In the link I posted, someone speculated that perhaps after crossing the EH, it would seem to recede from you at greater than c. So if you pointed a beam of light "behind" you, that light would never reach the EH. It is an event horizon even from within. If there is a direction toward the EH, the singularity is still also in that direction because that's what the light's going to hit!

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I think that length contraction comes into play here.

If you imagine 2 observers falling into a BH together, and just as approaching the EH one accelerates away (assuming it has unlimited energy resources) to remain stationary while the other continues free-falling, then the difference in speeds of the two observers must be near c? So the distances they measure will be severely length contracted. I might be wrong but I think the "stationary" observer will now see the EH as far away, as the length stops being contracted. The EH would again have to appear "frozen" to an observer stationary relative to it? An observer can't hover at the EH, but can it get arbitrarily close? Anyway, no matter how close or far, if you dipped your hand (or a long rope) in, you couldn't possibly get it back!

 

very length contracted, yes.

 

Near the horizon, inches in Schwarzschild coordinates (which are static) correspond to miles in free fall coordinates. In other words, a static observer sitting just outside the horizon would measures inches between two radii, but the same distance is miles to someone in free fall in the same area.

 

I'm pretty sure the horizon would be infinitely time dilated and redshifted to an outside observer regardless of the outside observer's motion. The situation is different for an observer at the horizon. They wouldn't see the universe infinitely blue shifted and infinitely sped up unless they applied infinite acceleration and remained static at the horizon, which of course they can't do.

Edited by Iggy
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Note: One thing I've realized I got wrong in earlier posts is assuming that light cones are conical through all of spacetime, but I think that's only true locally (or in flat spacetime)???


Near the horizon, inches in Schwarzschild coordinates (which are static) correspond to miles in free fall coordinates. In other words, a static observer sitting just outside the horizon would measures inches between two radii, but the same distance is miles to someone in free fall in the same area.

 

Schwarzschild coordinates use the local coordinates of an observer at an infinite distance, right?

The proper distance from any stationary external observer, to the EH... is it infinite?

I've read that the proper time of a free falling observer, to reach the singularity, is finite; is that only because proper lengths "near" the EH become length-contracted to nothing as the EH passes the observer? If so then if you remained stationary outside "near" the EH, any stationary ruler no matter how long would not reach the EH. You could not "dip" a hand into the EH at low speed (ie. unless it's effectively falling in).

 

Edit: Nope, I have no idea what I'm talking about here... https://en.wikipedia.org/wiki/Event_horizon says the proper distance from a stationary observer is finite.

Edited by md65536
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  • 3 weeks later...

Well an even horizon is just where light can't escape right? And IMO that makes it where light ceases to be useful as a medium for observation. By that I mean we observe things with our eyes, but if light stops being useful inside of the event horizon.. then its services are no longer required. Sort of like our ears when underwater, not very useful except when using radios, microphones, and headphones.

 

At that point maybe you would want to have gravity measuring technology calculating an image and electrically piping it into your visual cortex, so that you can actually visualize what is going on.

 

I has no idea on what the images of the inside of the EH would look like.

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