B Can we see 2 black holes orbiting each other?

[HansH]

Thanks, that helps. of course the discussion should not concern a connection between the brain and GR. I only used it to be able to generate a way to introduce a change at t=t1 to make the system remains as a collapsed star of further contract to form a black hole. so lets not talk about biology or neuroscience.

basically I started the thread to hope to get some better understanding how the situation evolves starting at the moment that the critical mass is reached and the process of collapsing is started. and especially how that evolves further down into the black hole and further into time. and for 2 merging black holes I was also wondering how that process evolves. Not sure if that can be explained a bit high level (the trouserlegs example was already such explanation) without the need to go into all details which would require a few years of university study first to get that theory digested.

 

[PeterDonis]

I started the thread to hope to get some better understanding how the situation evolves starting at the moment that the critical mass is reached and the process of collapsing is started. and especially how that evolves further down into the black hole and further into time. and for 2 merging black holes I was also wondering how that process evolves. Not sure if that can be explained a bit high level (the trouserlegs example was already such explanation)

As far as the merger goes, yes, the trouser legs is the best simple illustration that can be given at the "B" level.

As far as the original collapse process that formed the holes, it's not a question of "critical mass" exactly (though mass limits do play a role--see below), it's a question of what can hold the original object up against its own gravity to prevent collapse. What that thing is, and how it works, depends on the kind of object. Roughly speaking, there are four categories:

(1) Planets and similar objects, which are held up by ordinary atoms resisting compression. They can stay in such a state indefinitely. However, such objects can only have masses small enough that fusion reactions are not triggered inside them; if they get large enough for fusion reactions to start, they become...

(2) Stars, which are held up by thermal pressure of hot gas, heated by fusion reactions in their cores. They can only stay in such a state as long as the fusion reactions continue; once fusion reactions stop, they collapse into one of the two further categories below.

(3) White dwarfs, which are held up by electron degeneracy pressure. They can stay in such a state indefinitely as long as they don't accrete enough mass to put them over the Chandrasekhar limit of about 1.4 solar masses. If they go over that limit, they collapse, possibly into...

(4) Neutron stars, which are held up by neutron degeneracy pressure. (There are speculations that there might be other states of strongly interacting matter inside at least some neutron stars, such as strange quark matter, so "quark degeneracy pressure" might be a better general term, but that's not important for our discussion here.) They can stay in such a state indefinitely as long as they don't accrete enough mass to put them over the maximum mass limit for neutron stars, which is somewhere around 3 solar masses.

Objects that collapse into black holes generally start out as stars which are too massive to collapse into white dwarfs or neutron stars.

 

[HansH]

Thanks for these further overview. Of course it is good to know these 4 options. (for me this was not really new but good to have the overview)
For me at the moment I am really interested in the collaps process or merger process itself and If I can understand that a a high level, so it is sufficient to know that there is at least a method to let it collapse to be triggered by a simple press on the button and neglecting all the rest of the universe around that is not domanant for starting the process, which I represented by the rocket example.

one thing I am not certain about is the question if it is possible to represent this process of collapsing in a causal way, so suppose I press my button at t=t1 (for the ease of the example assuming then at t=t1 the collapsing process starts so the rocket is already very close when it is launched) how does it then progress go forward looking to the trouser example: does it then start at the part of the shoes (assuming they are close to the event horizon) and then wind up in time? and especially how does time flow from the shoes to above because spacetime falls inwards faster than the speed of light. imagining how that works is already a point on its own (ok probably this is also not the best way to describe but the best way I can think if at for the moment ) but at least it hopefully shows the point I am thinking about.

 

[PeterDonis]

For me at the moment I am really interested in the collaps process or merger process itself and If I can understand that a a high level, so it is sufficient to know that there is at least a method to let it collapse to be triggered by a simple press on the button

It's not that simple, since there is no way to, for example, accrete a significant amount of mass onto a white dwarf or a neutron star just by pressing a button (unless you also have a star's worth of mass lying around in a bin that your button releases). Nor is there a way to stop fusion reactions in a star's core just by pressing a button.

and neglecting all the rest of the universe around that is not domanant for starting the process

The collapse can be modeled as an isolated system, yes; the rest of the universe doesn't affect it appreciably.

if it is possible to represent this process of collapsing in a causal way

Of course. What normally causes the collapse, as I said, is something like fusion reactions stopping in a star's core, or a white dwarf or neutron star accreting enough mass to put it over the applicable maximum mass limit. These are causal processes. They aren't as simple as someone pressing a button, but that's true of most of the causal processes in our universe.

how does time flow

"Time flow" is not a good way of thinking about this. You have a spacetime geometry. That geometry is produced from some set of initial conditions, but thinking of that as "time flowing" is too simple.

For example, the "trousers" is a spacetime viewpoint. Yes, the "upward" direction (from shoes towards waist) is, more or less, the "future" direction of time, but, for example, mass falling inward doesn't go straight upwards in such a diagram, but it is still moving on future directed timelike worldlines. The collapse part would be down at the shoes, yes (below the shoes would be the object before it collapses), so the collapse is "in the past" with respect to the black holes that get formed, and those formation processes are in turn "in the past" of the merger (where the legs of the trousers meet). But that notion of "in the past" (basically, "towards the bottom of the diagram") is very general and leaves out a lot of important factors. It's the best that can be done at a "B" level, but it's still very, very heuristic.

spacetime falls inwards faster than the speed of light

No, in the viewpoint you refer to here, which is different from the "trousers" viewpoint, space flows inward around a black hole (it only flows inward "faster than light" inside the horizon). But you can't mix this viewpoint with the "trousers" viewpoint. They're different heuristic pictures, and both of them leave out a lot. In particular, the "space flowing inward" viewpoint can't handle black hole mergers at all (and isn't very well equipped even to handle the collapse of a single object to form a black hole).

 

[HansH]

Is there any graphical representation or animation available somewhere that gives an idea of how this process of merger or collapsing star to a black hole evolves in spacetime?

 

[PeterDonis]

evolves in spacetime?

Nothing "evolves in spacetime". Spacetime is a 4-dimensional geometric object that already contains the entire history of the system. So a spacetime representation does not show anything "changing" or "evolving".

As far as animations go, you might try Andrew Hamilton's home page:

https://jila.colorado.edu/~ajsh/

He has done a variety of simulations of various black hole scenarios. The basic idea of all of them is to pick an observer with a particular worldline in the spacetime, and show how things look to that observer as a function of their proper time along the worldline. He also has some spacetime diagrams.

 

[HansH]

Nothing "evolves in spacetime". Spacetime is a 4-dimensional geometric object that already contains the entire history of the system.

Yes of course, thinking about that I realize that there is indeed nothing to evolve as time is already in. But I also ralize that then the rocket that I decide to launch at a certain time can not be included in this system in this way, other than assuming the launched rocket is part of the 4-dimensional geometric object so the launching moment is on beforehand defined in the structure itself.

Basically this does not have to be a problem, as the effect of the launch moment is still fully visible in the 4D object.

so I could calculate the resulting spacetime as function of the launching moment. That actually adds an additional dimension to the structure which is all posible launching moments. Normally if you add a dimension to some structure all matrices, tensors etc then also get additional dimensions. However as you can probably see the 5th dimension as fully independent here (simply includes all possible spacetimes as function of the launching moment), I assume it doesn't give extra complications. (it does not make sense for example to look at the derivative of the launching moment having an effect on something else)

 

[PeterDonis]

the rocket that I decide to launch at a certain time can not be included in this system in this way

Sure it can. See below.

other than assuming the launched rocket is part of the 4-dimensional geometric object so the launching moment is on beforehand defined in the structure itself.

I'm not sure what you mean here, but as I said before, the case where the rocket is launched, and the case where the rocket is not launched, are two different spacetimes--two different 4-dimensional geometries. You can't have a single solution that includes both possibilities, because the spacetime geometries are different. But you don't need to have a single solution that includes both possibilities. You can just have two solutions.

I could calculate the resulting spacetime as function of the launching moment. That actually adds an additional dimension to the structure which is all posible launching moments.

No. If you change the "launching moment", you again change the spacetime geometry. It won't change whether a singularity is present (since if the rocket is launched, by your assumptions, a singularity will be present), but it will change other things about the geometry, because the spacetime geometry includes relationships like "when on Earth's clock the rocket gets launched". If you change when on Earth's clock the rocket gets launched, you change the spacetime geometry. So you don't have one "structure" with an additional "dimension" to represent the possible launching moments. You have as many different "structures" (spacetime geometries) as you have launching moments.

the 5th dimension

There isn't one. See above.

You are verging on personal speculation at this point. I would strongly suggest taking some time to work through a GR textbook to see how spacetime models are actually constructed.