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You have a series of masses, say 1 cm radius black holes (a bit more massive than Earth each).There's some threshold of (coordinate) separation where the line is either a series of distinct masses, or is one large mass (regardless of the number of them that you put in the line). So we presume the separation is greater than that, so they're spaced over 2cm apart. Any less than that and the mass of any pair of adjacent ones is greater than their mutual Schwarzchild radius since the latter is directly proportional to mass (well, at least for the two of them in isolation). So any finite line of these masses will have a Schwarzchild radius greater than the length of the line, and thus it will just be one big black hole.
So they're further apart than 2 cm. When the oncoming 2nd line of BHs comes on, for a moment they'll be one line with half the separation between them. Same story. If that new half-separation is under 2cm, both lines become one black hole and nothing gets out.
If they're one big black hole, then there's no meaningful coordinate 'speed of halting'.
Said photon was never inside any EH then, by definition. See my very first sentence of my first reply. You're positing this photon outrunning a null surface, which requires it to move faster than light, a self contradiction.
But with a long line of separate singularities inside that long black hole
It isn't a normal black hole, and it isn't a normal merger of two either. In a normal merger there are two singularities inside a single event horizon
This is something that may never have been explored.
[I like the list of "similar topics" underneath: Do white sheep eat more than black sheep?]
The correct answer involves coming up with a metric describing this that is a solution to Einstein's field equations, but that is beyond either of us.
But some naive reasoning may still apply.
When the oncoming 2nd line of BHs comes on, for a moment they'll be one line with half the separation between them.
High speed of passing doesn't help. If anything, that just adds energy and makes it more likely to be that one big BH
Quote from: David Cooper on 19/07/2022 19:10:13But with a long line of separate singularities inside that long black holeThere's no 'long black hole'. If you put the little ones close enough together, you get one black hole, and the event horizon of it is more or less spherical (assuming minimal total angular momentum). There's no such thing as a line of barely linked black holes. I spelled out why in my prior post, which perhaps you're not bothering to read. Tell me why my explanation is wrong if it is, but don't just keep repeating refuted stuff. I lay no claim to be necessarily right on this stuff.
QuoteIt isn't a normal black hole, and it isn't a normal merger of two either. In a normal merger there are two singularities inside a single event horizonNo. Per no-hair theorem, there's no external difference distinguishing one arrangement from another. Black holes have mass, charge, and angular momentum. They don't have different shapes due to internal arrangements of matter/singularities. Your entire line is in a one black hole. It cannot differ from another black hole with the same mass/momentum/charge. It cannot separate into two parts any more than a normal one.
QuoteThis is something that may never have been explored.Per above theorem, it has been explored, and proven otherwise.
As Halc and I implied in earlier posts - you do want to be using General Relativity and considering a solution to the EFE.
Assuming a set of black holes in close proximity remain as anything that would be recognisable or behave as a collection of ordinary individual black holes is a poor assumption.
So, exactly as has been stated in earlier posts - if a photon was on the wrong side of a genuine "event horizon" then it cannot ever reach an observer who was on the other side of that event horizon.
The sort of thing @David Cooper has been talking about would not have been a genuine "event horizon".
By definition there cannot be any event horizons which only temporarily constrain a photon but at a later time allow it to pass through and reach an observer who was on the other side.
We might just as well use a different co-ordinate system so that one black hole is considered to be stationary and only the other black hole is travelling. A similar argument applies to the long lines of black holes that David Cooper was considering - one of those lines can be considered as stationary.
However, you (David Cooper) seem to be intent on considering an encounter between two black holes where they are deliberately made to get too close to each other, i.e. where one black hole was almost on a direct collision course with the other black hole.
I think the notion of a "speed of travel" for a black hole is only useful and usefully defined for a distant observer and assigning a high or low initial "speed of travel" for black holes which do actually come into close proximity with each other makes very little difference to what happens locally around those black holes.
Anyway, how does this apply to the merging of two black holes? I don't think the "speed of travel" that the two black holes had initially tells you anything about what is happening locally around the black holes. It certainly doesn't affect their speed or movement through space that is local to the black hole. The "speed of travel" of a black hole is just something a distant observer can measure as described much earlier in this post and it is just an artifact of a particular co-ordinate choice. When and if the two black holes come into close proximity, I don't see how the two black holes can approach each other at a speed through local space that is anything other than c. In particular, I can see no reason to think that assigning the two black holes a high "speed of travel" initially is going to affect what happens locally where and when the black holes merge.
As I mentioned earlier, whatever happens here with external observations will be the same for LET as it is for GTR
This means that an LET analysis of events as these two lines of black holes approach each other is fully valid - all the action will map to the GTR analysis of the same action and provide the exact same 3D Euclidean view to the external observer.
If the line of black holes is infinite, they will never make that adjustment as there is an equal pull to either side on each singularity.
There is a difference, and it is already known that there is during black hole mergers where there are two distinct singularities within the same event horizon for some time as they cannot instantly become a single one at the moment of first event horizon contact. That will also show up in the gravitational waves.
.... we have a no-hair theorem: Stationary, asymptotically flat black hole solutions to general relativity coupled to electromagnetism that are nonsingular outside the event horizon are fully characterised by the parameters of mass, electric and magnetic charge and angular momentum. Stationary solutions are of special interest because we expect them to be the end states of gravitational collapse. The alternative might be some sort of oscillating configuration, but oscillations will ultimately be damped as energy is lost through the emission of gravitational radiation, in fact, typical evolutions will evolve quite rapidly to a stationary configuration.
ES said: By definition there cannot be any event horizons which only temporarily constrain a photon but at a later time allow it to pass through and reach an observer who was on the other side.DC replied: Your definition is a black swan rule. Don't let rules based on assumptions block your ability to explore what actual physics does.
ES said: I think the notion of a "speed of travel" for a black hole is only useful and usefully defined for a distant observer and assigning a high or low initial "speed of travel" for black holes which do actually come into close proximity with each other makes very little difference to what happens locally around those black holes.DC replied: If you want to understand the action, it's useful to imagine the speeds of approach and to understand that everything that needs to be done to halt the singularities must be done within a fraction of a second when measuring from the frame of reference in which you expect the unified black hole to end up at rest, while nothing can propagate faster than the speed of light in that frame.
You've mentioned LET several times. Is that Lorentz Ether Theory? https://en.wikipedia.org/wiki/Lorentz_ether_theory As far as I can see, this remains a fringe theory, with Special Relativity being the preferred mainstream theory. In 2012 there was apparently a viable Lorentz-invariant treatment of gravity added to the theory. https://en.wikipedia.org/wiki/Lorentz_ether_theory#Lorentz-invariant_gravitational_law . However, General Relativity still seems to be the preferred mainstream theory for gravity.
What you seem to have done is apply some results from special relativity only and not utilize whatever the LET version of a theory of gravity might be.
The idea of a "pull" or a force being applied is a Newtonian version of gravity. Gravity is not a force under General Relativity.
The problem is, I think, that you (@ David Cooper ) previously referred to an arrangement of one long line of singularities as being one Black Hole. You can't then blame Halc for assuming it was an ordinary Black Hole, i.e. an ordinary stationary solution of the EFE that is asymptotically flat.
It's a definition not a rule. It's also not "my" definition, the extract I quoted came from Wikipedia. That particular definition is based on something Rindler developed in about 1950.
I get the impression that in your analysis (which you stated is based on LET), the black holes are very much being considered as something like billiard balls moving through a fixed static space which seems to be described by the co-ordinate system in which the black holes are said to have a speed of approach.
In General Relativity something different can happen.
The black holes aren't just billiard balls moving through a static space. They are something which changes the nature of space around them.
As the two black holes approach each other they can be slowed down (or sped up) relative to each other because the metric of space between them was not describing flat space and futhermore it wasn't even static - it has been changing with co-ordinate time while the black holes approached.
So the co-ordinate separation between them isn't describing what it used to describe. The velocity vector of an object does change as it travels through curved space so the black holes can have their velocities completely changed while they are approaching each other.
The two theories map to each other perfectly when it comes to predictions of the visible action from outside black holes
but they diverge when describing the action inside them.
and this maintains Euclidean geometry while providing the same precision in its predictions as GTR.
the two theories are essentially mathematical transformations of each other (which is why some people consider them to be different interpretations of the same theory)
I won't go into the details here as this is not a discussion of rival theories.
The term black hole becomes fuzzy in such a situation, just as it does during part of the time when two black holes are merging and have linked up without their singularities yet merged.
In LET, the speed of light reduces, reaching zero at the event horizon
It differs significantly from your assertions, primarily in the existence of black holes, which is an Einstein-only concept.
They cannot exist in a preferred frame model since no coordinate system foliates all of spacetime.
Quotebut they diverge when describing the action inside them.Only by denying said action at all. There is no 'in them' in any preferred frame model.
You see to be making up your physics. I invite to to cite sources for your claims, and not sources from science denial sites.
Quote and this maintains Euclidean geometry while providing the same precision in its predictions as GTR.This is the first assertion. If physical triangles (made of rigid rods say) have angles that don't add up to 180°, it is hard to argue for Euclidean geometry. From where does this claim come?
LET is an alternate interpretation to only Special Relativity, never to GR.
QuoteI won't go into the details here as this is not a discussion of rival theories.But you've done so in making these assertions. Topic has been moved accordingly.
QuoteThe term black hole becomes fuzzy in such a situation, just as it does during part of the time when two black holes are merging and have linked up without their singularities yet merged.The verb tense usage here suggests there's a meaningful coordinate time at which what you picture as a pair of physical singularities merge after crossing each other's event horizons. I never suggested any such thing.
QuoteIn LET, the speed of light reduces, reaching zero at the event horizonHow can this object move at all through space? If the speed of light reaches zero there, the speed of matter would too, preventing a black hole from moving in coordinate space. It all seems self contradictory.
Again, a citation would be nice here since I doubt any of it comes from Schmelzer.
you try to hide the evidence
It is a matter of fact that the predictions of LET and GTR match up perfectly for all observations and experiments - there's already been a link in this thread to the wikipedia entry on LET which spells that out.
You may need to provide some references or more details for this.
I invite to to cite sources for your claims, and not sources from science denial sites.
You should not be a moderator because you deliberately sabotage discussions.
QuoteOnly by denying said action [within black holes] at all. There is no 'in them' in any preferred frame model.You get more irrational by the year. There are objects which science has discovered and called black holes, and they have event horizons. There is an inside and an outside of an event horizon.
Only by denying said action [within black holes] at all. There is no 'in them' in any preferred frame model.
You're the one making thing up here by misunderstanding things and misrepresenting my position.
The non-existence [up until apparently 2012] of a generalization of the Lorentz ether to gravity was a major reason for the preference for the spacetime interpretation.
It is not disputed by serious physicists, so what's your game?
QuoteQuote and this maintains Euclidean geometry while providing the same precision in its predictions as GTR.This is the first assertion. If physical triangles (made of rigid rods say) have angles that don't add up to 180°, it is hard to argue for Euclidean geometry. From where does this claim come?It comes from the fact (acknowledged on that wikipedia page) that the predictions match and that LET achieves this using Euclidean geometry with the speed of light slowing instead of trying to cram extra space into gravity wells while maintaining the speed of light at c.
Let me repeat: LET accounts for gravity by having light slow down in gravity wells, and this enables it to match up as perfectly to observations and experiments as GTR, so you're simply wrong.
You said,Quote from: HalcThere's no 'long black hole'. If you put the little ones close enough together, you get one black hole, and the event horizon of it is more or less spherical (assuming minimal total angular momentum). There's no such thing as a line of barely linked black holes. I spelled out why in my prior post, which perhaps you're not bothering to read. Tell me why my explanation is wrong if it is, but don't just keep repeating refuted stuff. I lay no claim to be necessarily right on this stuff.So, that had to be corrected, and it just added to your drive to hide this thread in the subforum bin dominated by mathematically illiterate ramblings where hundreds more of your errors are stored. You have to move my threads to hide your errors just as much as to defend the establishment's broken models.
There's no 'long black hole'. If you put the little ones close enough together, you get one black hole, and the event horizon of it is more or less spherical (assuming minimal total angular momentum). There's no such thing as a line of barely linked black holes. I spelled out why in my prior post, which perhaps you're not bothering to read. Tell me why my explanation is wrong if it is, but don't just keep repeating refuted stuff. I lay no claim to be necessarily right on this stuff.
QuoteHow can this object move at all through space? If the speed of light reaches zero there, the speed of matter would too, preventing a black hole from moving in coordinate space. It all seems self contradictory.As I mentioned in an earlier post, the speed of light is slowed relative to the black hole - not relative to the space fabric.
How can this object move at all through space? If the speed of light reaches zero there, the speed of matter would too, preventing a black hole from moving in coordinate space. It all seems self contradictory.
Quote from: David Cooper on 23/07/2022 19:41:52you try to hide the evidenceDo you really think that's what he's doing? This forum isn't hidden.
Hi.Quote from: David Cooper on 23/07/2022 19:41:52It is a matter of fact that the predictions of LET and GTR match up perfectly for all observations and experiments - there's already been a link in this thread to the wikipedia entry on LET which spells that out. I'll take responsibility for putting that reference in. However, it doesn't state that LET and GTR match up perfectly. It only states ... it is not possible to distinguish between LET and SR by experiment...
Halc and I have asked for references a few times now, I think .....
Quote from: David Cooper on 23/07/2022 19:41:52You should not be a moderator because you deliberately sabotage discussions. I'm not a moderator and I wouldn't want to be. However, you've got to see that the moderators have some obligation to follow some rules and policies.
The "new theories" section isn't the same thing as the "dustbin", it's just where any new theory is supposed to be discussed. If Einstein had posted his first draft of STR then it probably would have started in the new theories section. The main criteria for a discussion in the other sections is that it should be discussing what is considered to be the mainstream science of today.
Your posts were using some vocabulary that has an established meaning (e.g. "event horizon" as discussed in post #29) but you were directly stating that you were setting your own definitions and rules and just using the same terms anyway. That's OK but you can't then argue that you are discussing mainstream science. What you are doing is likely to accidentally or deliberately mislead people by using common terms to describe different things.
It's a standard way of putting things where they will hardly ever be seen by anything other than bots, so yes.
This is using Einstein's model, not a preferred frame model. To my knowledge, no preferred frame model has an event horizon at black holes since there are no events on the other side to define one. I may be wrong about this, so kindly put in the citation. Your lack of citations reduces your posts to mere assertions. LET does not make the claims you ascribe to it.
Misunderstanding your position isn't 'making things up'. You asserted valid physics in Euclidean space. You asserted action (or even space at all) within black holes in a preferred frame model like LET. I need references for those claims, else you very much indeed are making up your physics.
I'd not have moved the thread just for saying what LET theory posits, but you seem to simply be attaching the LET label to your personal ideas. That puts the topic here in new theories.
Wiki says an entire century went by without LET having a theory of gravity. The one in 2012 is not called LET as far as I know, and it does not back your claims as far as I know, but I invite your to prove me wrong.
In particular, when does say an infalling particle actually get inside a black hole? How long does it last there? These questions are meaningful in an interpretation with absolute time.
QuoteIt is not disputed by serious physicists, so what's your game?I'm disputing your personal claims, not disputing anything on which serious physicicts have commented.
Wiki says nothing of the sort. I'm looking at the LET page ES linked. Kindly quote the text you think says this. The article I see says LET doesn't have a theory of gravity at all, per the line I quoted above. It says nowhere that LET is a mathematical abstraction of GTR.
QuoteLet me repeat: LET accounts for gravity by having light slow down in gravity wells, and this enables it to match up as perfectly to observations and experiments as GTR, so you're simply wrong.Perhaps so, but citation needed. It certainly doesn't say that on the wiki page, which actually says that LET doesn't account for gravity at all.
This fails to tell my why my explanation is wrong,
and didn't even bother to quote the explanation itself.
Your purposes seem to be evangelism and not actual science.
A scientist would back his claims, and would demonstrate how erroneous explanations such as the one you didn't quote above are wrong. Instead I get raving assertions of conspiracy.
Sounds then like relativity. In an absolute interpretation, speed is relative to the absolute frame an not to any other.
Schmelzer seems to have solved this issue, but seemingly not by the premises you're asserting.