1

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 25/07/2022 23:48:50 »

Hi.

This is all about doing and discussing science properly while maximising the utility of the forum for readers and putting the right ideas and questions in the right places for them to find them with minimal effort.

   I quite like this forum but I think you might be over-estimating the readership.  For example, most people lecturing or actively engaged in research in Physics don't make a routine of logging in to this site on a Monday morning to discuss what's new in it with other members of staff.   Their time is better spent checking the new research papers that come through the established journals and they still can't be expected to check everything.  So some major developments won't come to their attention for several years.   If something is important then it will be mentioned in more than just one paper and might even come up as a topic of discussion in some conference.
    What do you think the readership of this forum is?  Who are you trying to get this information to?
    In one of your earlier posts you asked if someone has suitable simulation software to test something.   If you really want to attract the attention and expertise of someone with that sort of software then the "new theories" section is probably exactly where your post needs to be.   The average reader of the main sections isn't some Physics professor looking for information about .... how an oscilloscope works, or  indeed, if a photon can escape from a black hole....  they have access to textbooks, libraries and email they can send to other experts if they want answers for that sort of thing.   Quite possibly the best chances of getting your thread noticed by that sort of person would be to have it presented in the "new theories" section.

Well, we'll never know if that last bit's the case, but most readers of the forum look at new theories once and once only.

    I'm sorry if you feel your time was wasted.  Everyone who has spent some time here adding replies is suffering the same fate.   I know I put in a few hours trying to create some good replies including diagrams and animations.   Halc's replies also look like they took him some time.
    Overall this forum is a forum.  It's a place for discussion with others and also where some questions from the general public could be posted and hopefully answered.   It never was intended as a place to host some monologues or anything that might be remotely like a repository of authoritative articles.   There are some forums that will try and do precisely this but Naked Scientists doesn't have any such repository.
   If you were trying to deposit something like that here, then you are wasting your time.   It would be better to set up your own website (there are some freely available services, I believe) then the content stays put and has the same URL for ever (or as long as the service provider lets you have it, or stays in business   etc.)
     It hardly matters which section your thread is put in.  Once it gets old and falls off the 1st page of the board because newer threads have appeared -  then it will rarely be read by anyone ever again anyway.

Best Wishes.

2

The Environment / Re: Is global warming man-made?

« on: 25/07/2022 01:15:54 »

Hi.

Is global-warming man-made?
    Yes, if you want a simple answer.
Usually, I'd like to talk for a while about the evidence and the possibilities that it might be something else.   However, that will only confuse and detract from the main message.  So let's just go with clear  "yes, it is man-made".

Best Wishes.

3

Just Chat! / Re: New Member from United Kingdom

« on: 25/07/2022 00:37:52 »

Hi and welcome.

    Due to the number of people (or robots?) that just set up to spam the site, you might not get many replies to such a simple introduction.  However, if you are a human being and interested in using the site genuinely, then you are genuinely welcome.
    Try starting a new thread and posting your own question or joining an existing thread.

Best Wishes.

4

New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?

« on: 24/07/2022 02:07:54 »

Hi.

I liked the post @evan_au .

I have heard that the mathematician Gauss had a reputation for working on a mathematical problem until he solved it.

   Yes, apparently Gauss gave up mathematics when he found he was too old and he couldn't go longer than about 6 hours without his mind starting to wander a bit.   (My mind wanders a bit after 10 minutes).

About a non-educational proof:
   The Riemann Hypothesis is very likely to be one of those things where we would learn more by seeing all the techniques that were tried but failed to prove the result.    If there is a final proof of the hypothesis, then it is likely to be very specific to this problem and may provide no transferable methods or techniques - i.e. nothing that would be especially useful to solve any other problem in mathematics.

    However, the link you provided to a definition of a "non-constructive proof" is really describing something else.   It isn't necessarily that there isn't any educational value in the proof.   Instead, it's just that the proof focuses on establishing just the existence of something without necessarily providing any method to actually find the object of interest.   Providing non-constructive proofs is a bit of a "fashion"  - but that's going to take too long to discuss in this post.  With computers there is now a renewed interest in providing more practical proofs in mathematics - things that will lead to algorithms for finding things.

Examples:
   The intermediate value theorem:  If f (x) is continuous on the interval [a, b] and Y is a value between f(a) and f(b), then there exists a number c ∈ (a, b) such that f(c) = Y .
   This is a common theorem and the proof does only what is required - it proves the existence of a suitable c∈(a,b).    However, it provides no practical method to actually evaluate c.   You might know that a suitable value must exist but your on your own if you have to find it.   The proof is "non-constructive" - it does not show any method you could use to construct (or find) this value, c, given a particular function f.

   The fundamental theorem of arithmetic:    Every Natural number, N, can be written as a product of primes raised to some power.   Furthermore that representation is unique upto changing the order in which you write the factors and perform the multiplication.
    This is another common theorem but the standard proof is much more practical.   It's a "constructive proof" or "construction proof" instead of just an existence proof.   The first part of the proof (establishing the existence of one representation as a product of prime factorisation) involves finding factors and progressively dividing them out.   If you were given a specific natural number like 10036 and had to find the unique prime factorisation, this is exactly how you would want to go about it.   So the proof does more than just show a unique factorisation exists - it shows you how to construct it.

Best Wishes.

5

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 23/07/2022 22:19:51 »

Hi.

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.

    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 .....

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.

     This doesn't mean just telling people what you think LET is supposed to be about.   It means finding a textbook, research paper or article and providing the details of that.   Ideally, you'll even provide the relevant page numbers.   Then the reader can go and check the source information directly themselves.
 
   Sadly, this does take up your time but it's essential in any academic discussion.    I took the time to try and find out something about LET even though you hadn't provided any references.   I took the time to find the exact page numbers people might need in a book by Sean Carroll in post #29   etc.     Halc took the time to find a paper on the arxiv print server and provide us the reference for that and (it seems) spent a while trying to check for similar papers about a treatment of gravity in LET.

You 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.

Best Wishes.

6

New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?

« on: 23/07/2022 20:44:00 »

Hi.

Perhaps we can get the proof by scrutinizing the functional equation.

   Maybe but that could take a long time.   The chances are it took several people a few years to piece that result together.   The fastest way to get the proof is likely to be getting to the library and finding the book.  The proof may not even be more than a few pages and it might even look quite easy - but that's the thing about Mathematics:   It often looks easy when you know how to do it.   However, getting there can involve multiple "dead-ends"  - time wasted in pursuing ideas that looked promising but ultimately lead nowhere useful.   Quite often there's a few steps where there is no good reason to explain why anyone would have thought that it was worth trying.

    If, like me, you can't easily get to a library, then you might prefer to make another search for the result on the internet.   Just be carefull to look for reliable and authoritative sources.  There are many supposedly complete proofs of the Riemann Hypothesis that are available online but most of these have been shown to be inaccurate.   These swamp the results you get in a simple Google search and just the process of searching for good information has already taken me nearly an hour.   Sadly, many of the reliable sources of information hold the articles and research papers behind a pay-wall  (you have to pay to view the article).

we are forced to appeal to the authority,

   No, you don't have to believe them because their "an authority".   However, it is obviously sensible and time efficient to check their proof first rather than trying to prove everything yourself from scratch.
   
Best Wishes.

7

New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?

« on: 23/07/2022 14:29:37 »

Hi.

Which part of the reference that you quoted contains the proof that zero of Riemann's zeta function can not have real part >1 ?

   The proof is not shown in that article,  just the final result is stated:


Riemann hypoth.JPG (80.23 kB . 1269x161 - viewed 529 times)

   The same result is stated in may other articles,  for example:
 

Zeros of the Riemann zeta function zeta(s) come in two different types. So-called "trivial zeros" occur at all negative even integers s=-2, -4, -6, ..., and "nontrivial zeros" occur at certain values of t satisfying
s=σ+it    
for s in the "critical strip" 0<σ<1

[Taken from   https://mathworld.wolfram.com/RiemannZetaFunctionZeros.html ]

    I can't find the paper(s) where the result was first proved and it probably wasn't just one paper but several papers each with a result over different parts of the critical strip.   

This book seems to be cited by many articles and apparently does contain a full proof of the result and it's where I would recommend you start looking.   I'm sure that will also cite the original paper(s) where the result(s) were first proved, if you're intersted in the history.

E. C. Titchmarsh, The theory of the Riemann Zeta-function, Oxford Science publications, second edition, revised by D. R. Heath-Brown (1986).

     That's a £120 book and it's not on my book shelf but if you have access to a library you might be able to find it.

Best Wishes.

8

Physics, Astronomy & Cosmology / Re: Can we utilise antimatter to store energy from solar power?

« on: 23/07/2022 00:34:27 »

Hi.

    Do they really call it a magnetic Klein bottle?    A magnetic bottle, a magnetic trap or something with magnetic mirrors - these are terms I've heard of.
  It just seems that if you're using a Klein bottle then the whole universe can be considered to be inside it.  That probably saves a bit of trouble and cost getting the positrons into the bottle.


Best Wishes.

9

New Theories / Re: what is temperature?

« on: 22/07/2022 22:52:03 »

Hi.

  Apologies:     There's no way I've read all the posts since I last wrote something here.   It's just a quiet day and I'd like to join a discussion.

Are you asking for an example of something people currently use but clearly don't understand?

    At a cursory glance, someone was asking for that (Bored Chemist ?) and someone was trying to provide examples (Hamdani Yusuf ?).    I think we can let Hamdani off the hook on that one and help out a bit.
    I don't have a crystal ball for seeing into the future but this seems like a safe enough bet:
Gravity   --->   This is a reasonable 21st century example of something we use but don't understand yet.   In particular we don't have a quantum theory gravity but it seems like a reasonable guess that there will be one.   If one is developed, it then seems undeniable that gravity wasn't exactly what we thought but we did have some models and approximations and were able to use it and even provide scientific and mathematical models for it that weren't too bad.

    About the rest of the thread:
   I'm still not sure where @hamdani yusuf  was going with this thread or what is left to discuss.   If you feel so inclined, it might be worth writing a short summary of what has been done so far and/or what you feel is missing or still needs to be done.    The thread is now 25 pages deep and if there were any new members joining, I'm sure they couldn't read all of that.

Best Wishes.

10

New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?

« on: 22/07/2022 19:06:36 »

Hi.

Let's say I make a conjecture that there's no zero of Riemann's Zeta function with real component higher than 1. Is this conjecture provable?

   I don't know.   How long am I supposed to spend checking it?
Many people have spent some years looking at the Riemann Hypothesis,  I don't really want to spend that long.

Best Wishes.

Late Editing:  Actually this one may not take too long.   I think it's already been shown that all non-trivial zeros are in the critical strip   ( 0 <  Re(s) < 1).   So if   Re(s) > 1 then s is not a zero of the Riemann Zeta function.
Reference:  https://en.wikipedia.org/wiki/Riemann_zeta_function#Zeros,_the_critical_line,_and_the_Riemann_hypothesis

11

Physics, Astronomy & Cosmology / Re: Can we utilise antimatter to store energy from solar power?

« on: 22/07/2022 18:46:27 »

Hi.

No problem separating them from electrons as they will traveL in the opposite direction in a magnetic field

   That separates positive fluff from negatively charged fluff.  To separate the positrons from the fluff needs a bit more precision which has an energy cost because you'll want to maintain some electric and magnetic fields.

you can trap them in a magnetic Klein bottle until you need them.

    I really didn't know it had be a Klein bottle.  If it's clean enough will that be OK?
In any case, they require a magnetic field to be maintained.   That seems like an energy cost again.

that's what I think @paul cotter  and the other earlier replies are getting at.  You can't realistically obtain OR store the anti-matter in a way that is likely to be efficient. 

Best Wishes.

12

New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?

« on: 22/07/2022 14:39:16 »

Hi.

Now we're back to the first question in this thread.
......    What makes Riemann's Hypothesis Hard to Prove?

     The usual methods aren't productive.  That's the short answer.

   You've already had some reasonable replies from @Bored chemist  and @evan_au  (all on page 1) discussing the possibility that it might be true but unprovable from the ZF(C) axiom system.   Equally, it might be false but not provably false in the ZF(C) axiom system.   
    As you've probably already realised, it only takes someone to find a single counter-example:  A zero of the function which isn't an even integer or has real part = 1/2    and then the conjecture has been falsified.    Since people have been trying for a few years, the chances are now looking good that the conjecture is true.   The main issue is whether this is provable.

The bigger picture:
     We are used to being able to phrase or set up a problem in Mathematics and then find a proof (or proof that it doesn't hold).   Some human bias is then inevitable, you leave school thinking that mathematics can probably solve every problem.   Yes, sure there may be some problems I can't solve but someone, somewhere, could probably solve it or given enough time and determination I might even be able to solve it myself  - That's the sort of impression you leave school with.
     You would not have been shown or taught examples where Mathematics could not resolve a problem.   There would have been little educational value in it.   As a consequence, people rarely consider how many statements (let's say statements in formal first order logic) exist but have no proof (or falsification).   We have Godel's theorem's, so we know at least some such statements exist but few people consider how many such statements exist.
      Early Mathematicians were fairly certain that the rational numbers were all that was important and irrational numbers either didn't exist or were just inconvenient things that appear in mathematics only occasionally.   They were, in some sense, wrong.   The irrational numbers vastly outnumber the rational numbers (I know you've started other threads where the comparison of the cardinality of these sets has been discussed, so I'm not going to bother giving references for that).   Anyway, despite the seemingly overwhelming chances that numbers appearing at random would be irrational, it was possible for those early mathematicians to build incredibly powerful systems of mathematics, solve many problems that appeared in real life and improve the science and technology of the time.   They did all of that while skirting around what the majority of the Real numbers actually are.
        In a similar way, the number of mathematical statements*  that are NOT provably true or provably false from a given axiom system may be much larger than we had thought.

 * Mathematical statements  --->  statements constructed from a formal system of symbolic logic.   Reference:  https://en.wikipedia.org/wiki/Mathematical_logic#Formal_logical_systems ).

Best Wishes.

 

13

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 21/07/2022 19:41:37 »

Hi.

As I mentioned earlier, whatever happens here with external observations will be the same for LET as it is for GTR

    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.

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.

       You may need to provide some references or more details for this.   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.

For example, you stated this:

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.

     The idea of a "pull" or a force being applied is a Newtonian version of gravity.   Gravity is not a force under General Relativity.

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.

    The exact details may not be entirely right but the general idea is actually OK.   @Halc mentioned the no-hair theorem but this actually only applies to what are recognisable as conventional stationary Black Hole solutions and not to the unusual sources of gravitation that exist just before two black holes have merged (for example when gravitational waves are present).
 

.... 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. 

[Extract taken from p. 238,  Spacetime and Geometry,  Sean Carroll ]

   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.

   This brings me to another point about definitions and the use of existing terminology:

  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.

    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.
    The physics is safe - if there is some physics to explain then it can be done by describing it with another term like  an "orange horizon" or something else.    However, if you use the term "Event Horizon" then people will (and they did seem to) think you were describing the thing that is given by the definition much as described in that Wikipedia article.   Actually there are other definitions of an "event horizon" that you could use - but if you are doing this, then you would be advised to set out the definition you are using because the definition as set out by Rindler (approx. 1950) is the mainstream definition.

- - - - - - - - - - - -

  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.

   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.   

Best Wishes.

14

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 20/07/2022 03:08:19 »

Hi again.

   So @David Cooper  has repeatedly asked if the speed of travel of a black hole can make a difference to whether the singularities will ultimately merge when the two black holes are made to pass close to each other.

   There have been a few replies based on various things and everyone has basically said  "no",   the most important thing would seem to be how close the black holes get.
    Let's qualify some of this:  In the big picture I don't see why we need to worry about both black holes having high speeds of travel.   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.
    We do expect the speed of travel of a black hole to have some effect on the process of the two black holes merging.   If the incoming black hole has a high speed of travel then you'd expect the two black holes to orbit around each other for longer and at a greater distance,  steadily losing energy through gravitational radiation until eventually the conventional merging process is observed.   If the incoming black hole had a very high speed of travel and it doesn't pass too close to the other black hole then they might even have a hyperbolic encounter and the incoming black hole escapes to infinity and never merges with the other black hole.   Additionally, if the incoming black hole had a high initial speed of travel then you'd expect the final merged black hole that is produced to have more spin (angular momentum).  So there are some ways in which the speed of travel of a black hole would affect the merging process.
   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.
- - - - - - - -

How fast does a black hole move?
   Let's consider a large region of empty space with just one simple black hole in it.  So this is going to be described with the Schwarzschild solution.   Now I did say empty space but I'm going to want an observer in it, as usual we'll assume they are of such small mass that they don't affect the solution of the EFE at all.
    We'll have the observer at a large distance from the black hole and without wasting too much time, we'll have them use the Schwarzschild co-ordinates to describe the space around them.   So the black hole is stationary, it's not moving through space, as far the observer is concerned.   The black hole retains a constant set of spatial co-ordinates at all times.   The "speed of travel" of that black hole is 0 for the distant observer.
    If we want to consider a black hole that is moving through space, that's easily done.   We'll just have the observer convert the spherical co-ordinate system they were using  (t, r, θ, φ) that was based on the Schwarzschild co-ordinates into a Cartesian system  (t, x, y, z) centred around the observer and then apply a Lorentz boost to that co-ordinate system.   So to paraphrase this,  we don't really need to give the black hole any movement we can just have the observer move through space instead and use a new co-ordinate system in which the observer would still consider themselves to be at rest.   In this co-ordinate system the black hole has a "speed of travel" through space that is not 0 as far the observer is concerned.
    The "speed of travel" of a black hole is just a co-ordinate dependant thing, it depends on the co-ordinates that a distant observer was using.   That's nothing special or unique to black holes, we can say the same about any object that is distant from the observer and might be moving.   The objects speed depends on the co-ordinates that the observer is using.   All we need to keep in mind is just that the "speed of travel" of a black hole may not be telling you as much as you might have thought.   It is just telling you something about how the co-ordinates that a distant observer might assign to the black hole change with time.
    Now if space is just flat Minkowski space, then when an observer changes the frame of reference they use, it does result in a distant object moving through less (or more) of what the observer considers to be static space in exactly the way you would expect.   Specifically, the frame of reference can be extended to cover the region of space around that distant object and then the distant object has a certain speed through that bit of space local to it which will be exactly what you'd expect.   For example, if in one frame of reference, the distant object had a velocity, v, through the space local to it, then the observer can boost to a new frame of reference with offset velocity v and then when they examine that distant object it will have 0 velocity through what the observer now considers to be the static local space around that distant object.
     However, the same does not hold for Black holes and it is simply because space is certainly not flat Minkowski space when you get close to the black hole.   In General relativity you can't extend an inertial frame of reference to cover all of space.   However, all is not lost:   At every point in spacetime you can always find a local inertial frame.   So let's just start by having the distant observer try to use a co-ordinate system where we would naively think that the black hole is moving as slowly through space as possible.   Let's have the black hole have 0 "speed of travel" for the distant observer - that can be done by having the distant observer describe space with the Schwarzschild co-ordinates as set out earlier in this discussion.
     Now let's have a point, p, that stays on the event horizon of the black hole and let's set-up a local inertial frame there and see how fast that point must be moving through the space that is local to it.
EDITING:   This post is already too long, let's not do it but instead just refer any reader to standard texts on the Schwarzschild solution and just jump straight to some diagrams like all the Pop Sci articles would do.
   The Schwarzschild solution can be thought of as if space is flowing across the event horizon and towards the singularity.   Here's the diagram:

   
Here's a more relevant, if less aesthetically pleasing, diagram:



At the event horizon, the local space is flowing across the event horizon at the speed of light, c.   It will be more useful for us to consider this the other way round:  The event horizon is moving through space, it has the velocity c  through the space that is local to it.    This is how it will be in EVERY local inertial frame you set up around the point, p, that stays on the event horizon.   You can try to find another local inertial frame, for example, by applying a Lorentz boost but it won't help.   If something has the speed c  in one inertial frame then this is an invariant,  it will have that speed in EVERY inertial frame.    Just to phrase this more strongly:   You cannot find a local inertial frame centred on a point on the event horizon where the event horizon is travelling at any speed other than c.

   Now let's step back a moment to consider what effect the "speed of travel" that a distant observer might have assigned to a black hole can have on what happens locally around a black hole.   Well.... basically....nothing.... it makes not a jot of difference as far as I can see.   Any local inertial frame you set up on the event horizon will show you that the event horizon is moving through space at the speed c.     The distant observer might naively try and slow that down by boosting to another frame of reference and changing the "speed of travel" of the black hole but it doesn't help.   There's nothing you can do with the local inertial frame at the event horizon, you can try and boost that in the same way as the distant observer boosted their frame but it doesn't help or matter at all.  There's no local inertial frame at the event horizon where it travels at any speed other than c.

     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.

Best Wishes.

15

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 19/07/2022 23:44:59 »

Hi again.

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.

     That much I agree with.  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.
    I wouldn't be trying to find a valid solution for the EFE in such a situation either and I'm not sure anyone would.   I had the impression that the models of what are just 2 black holes (let alone an infinite number of black holes) orbiting each other and then merging are usually just numerical solutions or approximations for the EFE in such situations and not an exact analytical solution.   BUT I'm no expert and maybe someone does have an anlytical solution for such mergers.   Even if such an analytical solution exists I'll bet it's idealised and applies to a very specific set of initial conditions and all we've been doing is generalising from this. (Evidence: We are still finding new things like "lopsided" mergers resulting in the final black hole being given a significant recoil velocity when the incident black holes had unequal masses and spins.    https://www.space.com/black-hole-escaping-galaxy-from-collision ).

But some naive reasoning may still apply.

   Yes, I'll go along with this and just try and keep an eye on where that reasoning might go astray.

When the oncoming 2nd line of BHs comes on, for a moment they'll be one line with half the separation between them.

    Of course, we don't know that.   The trouble with General Relativity is that when you move masses around they don't move to some new piece of space in a nice predictable way like Newtonian mechanics would suggest and space has been left unchanged.   In General Relativity, you can't avoid completely changing the nature of space when the mass is re-distributed.
    So, using a simple Newtonian view, it looks like there should be a moment when the two lines of black holes are just one line with half the separation between them  but in reality the metric is completely different at that time with the masses distributed in this way - so the separation between the black holes could be.... well... anything.

High speed of passing doesn't help. If anything, that just adds energy and makes it more likely to be that one big BH

   I very nearly said something like that - before deciding it just wasn't all that simple.   I completely agree with the sentiment, I'm just not sure that the speed of travel of a black hole is a good measure of any "energy density" that you would want to include in the stress-energy tensor.   In particular, it may not describe the kinetic energy of a black hole because it isn't really describing the velocity of any part of the black hole through the space that is local to it.
       @David Cooper  has repeatedly asked if the speed of travel of the black holes would make a difference and somehow allow the black holes to separate again or get past each other without merging.   This has never been an easy question to answer.

      If the two black holes approach each other and a shared, connected event horizon forms around what was previously recognisable as the two separate sources of gravitation,  then all of the people who have replied on this thread   (Halc, Bored Chemist and I) are of the opinion that there is no way that event horizon is ever going to separate again and leave what is recognisable as two separate black holes moving away from each other.
   We could argue this purely on the basis on what the formal definition of an "event horizon" is.   Halc mentioned this right in one of his earliest replies and Bored Chemist seems to have been consistently using this formal definition of what an event horizon should be.   
     In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer

[Definition taken from Wikipedia]

    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.    However, we can imagine a dynamic metric existing (one which varies with co-ordinate time such as a gravitational wave solution for the EFE),  so that there is a surface through spacetime where space is flowing past that surface at the speed of light for only a finite amount of co-ordinate time.   To say it another way, for a short amount of co-ordinate time, time-like paths across that surface can only take objects from region I to region II but not from region II to region I.   This, I think is David Cooper's notion of how a photon could be temporarily inside the "event horizon" but then re-emerge if and when the two black holes do manage to pass each other.      Formally, the photon was not inside a genuine "event horizon", it was only inside a surface where time-like paths did not exist to the region of spacetime exterior to the surface for a small amount of co-ordinate time.   I don't think there is any terminology that is commonly used to describe such a surface.     In summary, you  ( @David Cooper ) have led everyone to a certain conclusion by using the terminology "event horizon" and suggesting that the event horizons of two black holes could merge and form a combined event horizon for a while.    As stated in the very earliest replies, if a photon was on the wrong side of a genuine event horizon, then there isn't any calculation or carefull consideration that needs to be done - by definition it is never getting to an observer outside that event horizon.

   I was going to discuss how the speed of travel might affect the merger of two black holes but I'll do that in another post (if at all), since this one is already quite long.

Best Wishes.

16

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 19/07/2022 00:37:45 »

Hi again.

I can't keep up with the posts and respond to the issues systematically.   I'm just going to skip to some of the latest posts.

....  I've now found a situation where you can play with the strength of dark energy to change the size of a universe such that you can create an infinite line of black holes separated by vast distances, ....... You then have all these black holes moving along parallel paths throughout the rest of the experiment....

    You're doing an experiment?   I once mixed some baking soda with lemon juice and was amazed with the results but your experiment does sound more impressive.
  - - - - -
I think the next post may have answered this, you are looking for simulations...

If anyone has simulation software capable of checking it, they should be able to provide a definitive answer

   OK.   Regrettably I don't have any such simulation software.

Best Wishes.

17

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 18/07/2022 22:14:48 »

Hi.

If you are observing these and see the black holes approaching each other at these high relative speeds which you measure as a fraction less than c in opposite directions, you will also measure the event horizons to be contracted so strongly that they are almost turned into flat discs, exactly as a spherical planet would be when observed to be moving at such a speed.

   and also,

You can certainly calculate under both LET and GTR that the black holes look spherical to observers moving at the same speed and in the same direction as them

    There is a difference between how things "look" and how they are.  You might be mixing the two.
I agree that a Black hole looks like a sphere to a distant observer moving with the Black Hole.   However, it is not actually a sphere as you would imagine one in 3-D Euclidean space.   The distant observer knows this if they apply the right metric.   For example, the Schwarzschild metric for a black hole where I've set the Schwarzschild radius to 1 unit is given by:

ds² =     +  terms involving the other co-ordinates  t,θ, φ

    As I mentioned, the Schwarzschild radius was set to 1 unit and a distant observer might very well see the black hole as a sphere with a radius of 1 unit.   For large r  (a long way from the black hole) then the r co-ordinate does behave exactly like a measure of the radial distance from the centre of the black hole.  In the local region around the distant observer, these co-ordinates are describing space perfectly adequately and naturally:  To the distant observer (r, θ, φ) act like spherical co-ordinates describing flat space (the metric would be the ordinary Euclidean metric) with r as the radial distance from the black hole and θ, φ as the polar and azimuthal angle from the black hole.
    Now, if the distant observer plots the location of the black hole event horizon on a piece of paper using these as if they were spherical co-ordinates in ordinary flat space then they do indeed produce a plot where the black hole looks like a sphere with radius 1 unit centred at r =0.   
    However, the physical distance from  r = 1   to r=0    is not 1 unit of length  (i.e. the physical distance from the Event horizon to where the observer would naively consider the centre of the sphere to be located).   This is because these locations are NOT local to the distant observer and the metric has long since stopped approximating the Minkowski metric when r is small.

   The path length   from r=1 to r=0  (holding constant t, θ and φ) is determined (as usual) from the metric shown earlier:

     =   

   Since  r ≤ 1   throughout that integral we are taking roots of a negative quantity.   So the integrand is imaginary and hence the total path length is imaginary.    Most significantly, it is certainly not +1 unit, the Schwarzschild radius.

Best Wishes.

18

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 18/07/2022 03:19:43 »

Hi again,

I don't really need to worry about the "If".

   OK,  I was just wondering how best to start replying.   I don't want the replies to seem like outright disagreement throughout.   

Let's start as far back as possible:

Picture a situation where two black holes are moving in opposite directions at just a fraction under the speed of light. Their event horizons are length contracted so much that they practically become discs rather than spheres.

    No, I don't even agree on this.
    Firstly the black holes aren't intrinsically changed into discs.  At best that's only how it will be for a distant observer that is not moving with the black hole.   Moreover, the black hole becomes a "disc" only in some co-ordinate system which the distant observer KNOWS is almost completely useless in the region of space that is not local to the observer and yet they persist in assuming distances are determined by the Minkowski metric.   In particular the metric is very different around the black hole.     
   Special relativity only gets you so far,   let's do it and see:    Let's have a black hole moving along the x-axis and centred on it.  Let's have an observer fixed at x=0, they assign x-axis co-ordinates  x₁  and  x₂  to the two sides of the black hole at a fixed time.    The observer never learnt any General relativity so they assume the black hole has a width along the x-axis of  x₂ - x₁.    We'll have another observer but this one will be moving with the black hole along the x-axis but starting as usual at x=0 when t=0.   That observer assigns co-ordinates x₁'   and x₂'  to the two sides of the black hole and, exactly as you might expect from special relativity, x₂' - x₁' is going to be slightly bigger (slightly wider) than the other observer reported.     The second observer is only using special relativity so they will assume that the width of the black hole was  x₂' - x₁'.   We're done.... the two observers have different widths and the black hole looks like a disc to one of them and a perfectly round sphere to the other.
     Now let's add some general relativity:   The Minkowski metric doesn't apply when you get too far away from x=0 because the space between the observer and the black hole (and also across the black hole) wasn't flat Minkowski space.    So the distance between  x₁ and x₂ on the x-axis is NOT equal  to  x₂ - x₁    when x₂  and x₁  are far away from the observer and close to the black hole.
       So, just to be clear,  the two observers have a different value  of   (x₂ - x₁ )  and one observer has a smaller value but neither of these quantities was the physical width of the black hole anyway.

IS THIS IMPORTANT?   No, not on it's own.   It's just one example where not using general relativity can lead us off the tracks early on.     Just because a conventional solid object would show length contraction when it is moving relative to an observer (in flat Minkowski space) it doesn't follow that a black hole would show the same sort of length contraction.

Does a black hole become flattened and disc shaped when it is travelling relative to a distant observer?   I honestly don't know.   I know that it's not obvious.  Shapes aren't what you might have thought in curved and non-Euclidean space.   For example, even if a black hole is considered to be stationary relative to a distant observer, it's still not like a sphere as the distant observer would imagine one in 3-D Euclidean space.  A black hole has no spatial centre, there's no place in space where I can put the point of my compass and start to draw a perfect circle around the black hole.

Best Wishes.

19

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 17/07/2022 19:18:24 »

Hi.

Sorry, this is going several posts back....

Clearly if it's possible for the two black holes to pass each other at very high speed without merging if their event horizons touch.....

    I'm not sure what this sentence or group os sentences was saying.   There's an  "IF"   in it.    Are you asking if this is possible,  or is the IF an accident and you are telling us it is possible and then the rest of the stuff described in the sentence does happen? 

Best Wishes.

20

New Theories / Re: Can a photon escape from inside the event horizon of two black holes?

« on: 16/07/2022 23:36:34 »

Hi.

The two black holes pass each other in such a way that at the point of closest approach the edges of the two discs pass through each other.

     The first problem is that conventional Black Hole solutions  (e.g. Schwarzschild  or  Kerr–Newman Solutions)  just won't continue to apply (they won't even hold as a rough approximation) when two black holes come into such close proximity.
     As such it's not obvious that there would be two separate event horizons, or that they would pass through each other.   As the Black Holes approach each other, a different solution to the Einstein Field Equations would be exhibited.  I can barely guess what that might look like but our best models are going to be those used for orbiting black holes that eventually merge  (e.g. the sort of thing that LIGO has observed).   
     To paraphrase this,  a black hole is not a physical object like a big particle of matter.   It is a much more intangible thing,  it's just an unusual curvature in spacetime.   When two black holes get close we can't assume anything like two Black Holes continues to exist.   Instead you get a different thing, a new spacetime curvature appearing.

Now, if we have a photon moving perpendicular to that action (you should visualise this as moving straight upwards) such that it passes through the edge of both discs exactly at the moment when they pass through each other,...

     The problem is that there wouldn't be two recognisable EH discs in this region of space.   There should be just one bigger joined up event horizon surrounding an unusual gravitational source (a source that was previously recognisable as two separate black holes when they were further away from each other).
     Keeping everything simple:  Any photon that enters the region bound by that (new, conjoined and bigger) event horizon should not be getting out again.   (To the best of my knowledge - although I'm no expert in this.   With things like Hawking radiation, a similar photon might appear in the region around the event horizon if the two original black holes do manage to pass each other instead of merging and become recognisable as separate black holes again travelling away from each other).

Best Wishes.