Black holes

[Green Baron]

9 minutes ago, sevenperforce said:

Causality is not "hurt" because the gravitational field of the infalling object already existed. We can model the merger of two gravitational fields without difficulty.

I know. Just wanted to steer the attention to a possible problem that could arise with something seemingly happening (expansion of Schwarzschild radius) "before" the cause (additional mass of object inside of it). Because i expected that to be the next question ;-)

The linked text explains that quite nicely.

[YNM]

17 minutes ago, sevenperforce said:

Causality is not "hurt" because the gravitational field of the infalling object already existed. We can model the merger of two gravitational fields without difficulty.

Time dilation is the consequence of a difference in gravitational potential, not a consequence of spacetime curvature. The gravitational potential saddle point between two black holes has no gravitational gradient -- you're not going to fall in either direction -- but it is still located at a lower gravitational potential than an outside observer, and thus time will run at a different rate.

Ah, the classically inverted deltas... yes you're right. Been a long time since I see those !

[sevenperforce]

For the infalling observer, it is also important to note that there is a fundamental break between space and time. In our ordinary experience, time is not location or velocity-dependent. Time moves at the same rate if I walk to the east as if I walk to the west. But near the event horizon, time is no longer flat. The passage of time becomes a vector quantity, essentially.

So you can imagine the infalling observer as entering a region where time flows more and more toward the black hole. Physicists talk about this in the sense of light cones; since light travels at the speed of causality, the "future" light cone represents all future time interactions. As an observer falls through the event horizon, their light cone becomes larger and larger in one direction and smaller and smaller in the other direction, warping until there are no worldlines which go anywhere other than "down".

On the other hand, you can alternately imagine it from the perspective of space. Gravitational force can be represented as the acceleration of space itself; an observer falling into a black hole has space below him accelerating faster and faster while space behind him becomes smaller and smaller. As he crosses the event horizon, the rest of the universe shrinks to a single point and disappears while the interior of the black hole event horizon expands to fill all of (his) reality.

[Green Baron]

Oh, ok, what i read did not try to explain what happens "inside". Here you left me :-)

I apologize for my un-sciency and philosophically choice of words but, hey, this is a game forum and i am trying to use my own words on a complicated matter !

 

If we assume that as the spaceship approaches the Schwarzschild radius (Sr) and its time in relation to the universe runs faster and faster (it accelerates through the universe's time or crosses all the timelines of the universe) it is ever more shifted into the future of the universe until when really reaching the Sr is taken into the infinite future of the universe because it takes from the universe's reference frame an infinite time to cross the Sr. Am i still with me ? Now, could that happen in a closed universe ?

As black holes exist and they do grow but it takes infinite time seen from the universe to cross the Sr then there has to be an infinite future, no ? Which means that the universe cannot be a closed one that one day collapses again, that wouldn't be infinite and couldn't contain full featured black holes, right ?

This point is of course not mine, it's from the literature i found on the subject. But it has that aha ! aspect :-)

Edited March 27, 2017 by Green Baron

[sevenperforce]

17 minutes ago, Green Baron said:

If we assume that as the spaceship approaches the Schwarzschild radius (Sr) and its time in relation to the universe runs faster and faster (it accelerates through the universe's time or crosses all the timelines of the universe) it is ever more shifted into the future of the universe until when really reaching the Sr is taken into the infinite future of the universe because it takes from the universe's reference frame an infinite time to cross the Sr. Am i still with me ? Now, could that happen in a closed universe ?

As black holes exist and they do grow but it takes infinite time seen from the universe to cross the Sr then there has to be an infinite future, no ? Which means that the universe cannot be a closed one that one day collapses again, that wouldn't be infinite and couldn't contain full featured black holes, right ?

One feature of Lorentzian transformations and associated relativistic chicanery is that even though timestreams and simultaneity get completely twisted and swirled around, any reference frame can still be mapped to any other reference frame by applying the correct mathematical transformations. So it isn't possible to end up with something going "infinite universe" because it would be impossible to map that to the rest of the universe.

From the perspective of a distant observer, there is a defined point in finite time at which the gravitational field of the object and the gravitational field of the black hole merge, because the gravitational potential field travels at the speed of light. The problem is that while the merger of the gravitational fields can be observed (see LIGO, etc.), directly observing the object as it falls toward the event horizon requires light to be emitted by the object. But the light emitted by the object is redshifted more and more, both by its velocity and by its position inside a deep gravitational well, until finally the total radiation emitted by the object that reaches the observer reaches zero at the time when it actually crosses the event horizon as seen from the observer's location.

[Green Baron]

49 minutes ago, sevenperforce said:

One feature of Lorentzian transformations and associated relativistic chicanery is that even though timestreams and simultaneity get completely twisted and swirled around, any reference frame can still be mapped to any other reference frame by applying the correct mathematical transformations. So it isn't possible to end up with something going "infinite universe" because it would be impossible to map that to the rest of the universe.

? ton yhW

What is the problem with infinity ? Lorentz is not involved here. It is simply that where the universe closed (time limited), then a full featured black hole with an event horizons could not exist because it requires objects/radiation that meets its Sr to go to infinity in the time frame of the surrounding universe.

I try another choice of words: as an objects approaches the Sr its proper time goes through an increasing "amount" of time in the universe. The process is accelerated as the object comes closer to the Sr. From outside it looks like the object is getting ever slower until it stops at the Sr (which cannot be observed as we have stated above). And that stop is the interesting thing because it means that in a very short proper time in the object the time around passes. If you want the time frames mapped: at the Sr passes in an infinite short proper time an infinite long universe time. Or, the object passes the Sr in every timeslice of the universe since the time of the universe is compressed to what we call the event horizon.

Or it is not an Sr or event horizon but something similar that behaves like one.

I again link to the Brown guy, another text because i doubt i can describe it correctly, but i can imagine that Wikipedia has something similar somewhere ...

Edited March 27, 2017 by Green Baron

[YNM]

@Green Baron @sevenperforce I supose transformations doesn't really have any problems with infinite size - all depends on what the resulting values in all points be. Much like how in the original coordinate / metric that Schwarzchild used the radius itself is also a singularity - later another choice of coordinates / metric shows that it's just an artifact of the coordinate used.

It is true that an infalling observer would see the universe evolves off much, much faster outside the black hole; However, the observer is "not that part" of the universe. Think about being able to see the farthest galaxies - if you were to be packed as a light beam and sent off to your destination (no ftl here) you'd see an era completely different than the one you saw from far away, and you'd see home totally in the different era than the one would be if you travel there. 

The same more or less applies to an observer falling down the black hole - it may well be that he will observe the demise of the universe outside him, and so the black hole's demise. But it has nothing to do with the fact that the poor chap is, for all reasons, been "inside" (part of) the black hole already, from a viewpoint of an outside, far away, calm and cozy observer back home. Causality isn't that strict, esp. when only one party can affect the other but not the reverse.

Let's... just say it's a lot complicated to talk about observers falling into a black hole 

Edited March 27, 2017 by YNM

[sevenperforce]

Indeed. Less and less of the outside universe is visible as you go farther and farther in.

[HebaruSan]

Does Matt O'Dowd lurk the KSP forums? Maybe!: