Markus Hanke

Obviously in most modern societies we are free to express pretty much anything we want (with notable exceptions, and with the caveat that some forms of speech will certainly result in consequences of various kinds). But - and let me play the devil’s advocate here - where does this fit into a larger picture? Is unrestricted freedom always necessarily a good thing, no questions asked? I hear so many people keep going on about their “right to free speech”, but very few ever talk about their corresponding responsibility to engage in ethical speech. People like freedoms, but they don’t like the responsibility that comes with it. If I say or do something that is deeply hurtful to a lot of other people, and is not conducive to peace, prosperity and well-being of society as a whole, in what sense is such a freedom to be considered ‘good’? Much has been said about people’s freedom to engage in whatever speech they want - but what about people’s freedom from forms of malicious or otherwise hurtful speech that is simply not compatible with a civilised and peaceful society that values the well-being of all its citizens? Before anyone responds, I’d like to point out that I grew up under a communist regime in the former Eastern Bloc, so I know first hand what it is like to live in a society that does not grant freedom of speech (well, theoretically you could say anything you wanted of course...but some things you were only ever going to say once, so effectively the freedom was severely curtailed). It isn’t just an academic concept to me, I’ve experienced it, and it is not a good thing. On the other hand though, I am also on the autism spectrum, and as such I am simultaneously more sensitive and vastly more conflict-avoidant that most neurotypical people. Some forms of speech with malicious intend, directed towards me, will affect me very deeply, and at the same time I am entirely incapable of confronting the speaker about it. So for everyone like myself, who is affected in different ways by harsh and malicious speech (essentially everyone who does not fully conform to the accepted norms of society) - where is our freedom from such forms of speech? Why is this never really debated? Given the choice, I would personally be very happy to trade some of my ‘freedom to’ for a bit more ‘freedom from’, if that is conducive to my overall wellbeing. Of course I am aware of the difficulties - who makes these decisions, based on what, etc etc...but still. I don’t have a very specific point to make, I just wanted to put this ‘freedom to’ vs ‘freedom from’ thing out there.

Many (but not all) galaxies are approximately disk-shaped to varying degrees, so these would be good examples. Another example that comes to mind would the accretion disk around a large black hole. Of course. Light must follow geodesics of spacetime, just like anything else that is in free fall (it doesn’t matter if they are massless or not). The most striking and obvious example of this would be gravitational lensing. No, because cosmological redshift isn’t the same as optical scattering or refraction, as Janus has pointed out above. More crucially, it is not the only phenomenon that would be hard to explain within a static universe. To put it simply, if we consider all available data (not just a single isolated phenomenon such as redshift), then the Lambda-CDM cosmology is by far the best model that can explain them in one coherent framework, which is also compatible with everything else we already know about physics.

No, it’s simply about describing the world around us in terms of suitable models. When I do General Relativity (one of my main areas of interest within physics), I think of spacetime is a network of relationships between events; in some sense that is quite real, because we can go and (at least in principle) measure these relationships directly with clocks and rulers, and what we find is in excellent agreement with the model. I do not look at spacetime as some kind of ‘thing’, as an ephemeral substance that is somewhere out there, akin to some old ideas of aether. If anything at all, its fundamental nature is information, namely relationship networks. Like you, I am also interested in the question as to the true nature of things - but I do not expect the answer to come from physics alone. Firstly, there is a big question mark over what the concept of ‘true nature’ actually means - how do we know that there necessarily even is such a thing, that it is a meaningful concept? Our intuition as human beings tells us that there should be, but intuition is very much fallible on such matters. Secondly, who is to say that ‘true nature’ of the universe - even if it is a meaningful concept - can be known in an epistemological sense? Perhaps it is a phenomenological endeavour, meaning it can only be known through direct experience and insight, but not through intellectual knowledge alone - which is of course what many of the Asian philosophical schools teach. So I personally believe that a complete understanding of the human condition (which of course includes the universe as a whole, since we aren’t separate from that) requires a synthesis of all the various domains of enquiry - the physical sciences, philosophy, social sciences, spirituality etc. These domains are not separate, they just ask different questions about different aspects, and answer them using different methodologies, which is fine so long as they yield constructive answers. I would really like to see these domains supporting and informing one another more, a coherent attempt to better understand who we are within the wider universe. It seems to me that one of the great tragedies in the history of the human race is that understanding the human condition somehow has become a partisan issue - science vs philosophy vs religion vs....you get the idea. I would never expect a complete understanding to arise from anyone of these domains in isolation, and that includes physics. But I also have no doubt that physics will have a central part to play, due to the nature of what it concerns itself with. Yes, and over time more and more data became available, and people began to realise that this model just didn’t do a very good job in predicting certain phenomena that could be observed. So eventually it was abandoned for something that worked better (all the politics and religious fanaticism that was involved aside for now). So physics is a continuous process of refinement - you keep evaluating existing models against new data that becomes available, and if something doesn’t fit, you either adapt the model, or come up with a new one that can explain things better. So over time you come closer - step by little step - to the underlying ‘true reality’ you seek. This process is in full swing currently, because we already know that there are certain situations where our current models fail, for example gravitational collapse, or the very early universe. We can be fairly certain that our current understanding of spacetime and all the various phenomena in it is only an effective approximation to something more fundamental, and many efforts are underway to find out what that is.

With all of the above being said, I think is also important to remember that the property of mass only exists at all because the universe is now in a state of comparatively low energy. If you go back to the early universe, prior to the point of electroweak symmetry breaking, the Higgs mechanism did not yet operate, so all elementary particles were massless. In that sense, mass is just the result of a broken symmetry.

The geometry of spacetime in and around a flat (presumably disk-like) distribution of energy-momentum is very different from the one of a spherical distribution - so the difference would be immediately obvious simply by considering the motion of other bodies (and light) in the vicinity.

Physics doesn’t seek to ‘understand the true nature’ of things (that would be more of a philosophical or at best metaphysical endeavour) - it only seeks to make descriptive models of natural phenomena, formulated in the language of mathematics. Spacetime in particular is a descriptive model of the motion of test particles under the influence of gravity, as well as the relationships between clocks and rulers in different reference frames. Oftentimes, having a description of how something works also helps to illuminate why it works that way, but that is not necessarily always the case in physics. There really is nothing wrong with a utilitarian approach, in my opinion - even if it sometimes fails to satisfy our curiosity. I personally think that demanding physics to provide answers that are actually beyond its intended domain of applicability is far more dangerous and problematic.

There is nothing here that needs to be refuted - spacetime is a mathematical model, a description of certain aspects of reality, in the same way that a map is a description of some territory. Would you argue that maps don't mean anything, just because they are not identical to the territory? Of course not. Instead, you ask to what degree of accuracy they reflect the real territory, in the sense that whether or not the map can get you from A to B without you getting lost. If it can, then it is a good map, if not then it needs to be discarded or revised. The concept of spacetime is no different - does it accurately model the dynamics of test particles under the influence of gravity (or in relative motion, or both)? Within its domain of applicability, it evidently does a pretty good job at that. There are other examples of this in physics, like electromagnetism, or thermodynamics. This is not how it is understood at all. It's a mathematical model, not a 'real thing', whatever that even means.

Because any conceivable clock - even an ideal one - must be massive, and therefore it cannot be comoving with a photon. Mathematically speaking, you can't parametrise the length of a photon's world line using proper time (because ds=0); however, that doesn't mean that their world lines don't have a well defined length in spacetime. They do, you just need to use a different affine parameter.

But what about entropy? If you consider - for simplicity's sake - a Schwarzschild black hole (i.e. empty spacetime everywhere), then how would it be possible to associate a notion of entropy with the horizon surface area, if spacetime enclosed by that horizon didn't have a microstructure of some kind?

Thanks, I might post it there, didn’t even think of that. I do not have access to a desktop computer (long story), so I’m afraid the trial won’t work for me.

Those are not ‘papers’, and length contraction is not a process of physical changes; it’s a relationship between frames in spacetime, as explained earlier. It’s nothing to do with anyone’s theories, it is just standard differential geometry - which is something you should be using when you talk about spacetime, because then misconceptions like this one won’t happen in the first place.

No, it’s a relationship between reference frames in spacetime, same as time dilation. All inertial frames are subject to the same laws of physics, so there are no changes in any of the fundamental interactions. Specifically, and quantum mechanics aside for the moment, EM forces can be considered as 4-vectors, which are invariant under Lorentz transformations, so all observers agree on them. What observers do not necessarily agree on, however, are the precise numerical values for each component of that 4-vector.

Lol...that was how I first started to teach myself coding. The good old ZX Spectrum with its squeaky tape drive. Oh the memories

I don’t agree. The largest colliders we currently have operate at around ~14TeV, this is nowhere near what is needed to definitively rule out String Theory and most other models with compactified dimensions - it’s in fact off by many orders of magnitude. But I do agree that the failure to detect any of the other Higgs particles within this energy range puts serious constraints on possible supersymmetry extensions to the Standard Model. In fact I don’t know of any SUSY models that contain Higgs bosons with more than around 10TeV, so if SUSY is really a thing, then we should have seen those signatures by now - but someone please correct me if I’m wrong on this.

Of course. No one is sure about this. In particular, no one is sure just how far exactly the domain of applicability of GR actually extends below the horizon. Sure, somewhere below the horizon as per yet unpredictable things will happen. But it won’t be as far up as the horizon itself. No. That a collapse happens is certain, at the very least up to energies of the QCD scale. The physics involved are well understood and thoroughly tested up to that point, in full accord with the scientific method. It’s only when we go beyond that (the last stages of the collapse) that we don’t yet know what happens. This doesn’t have an objective answer, since ‘complicated’ is a subjective term. I find GR conceptually easier than Newtonian gravity, even though it is more complex. But we already know that it doesn’t exist, that’s what I have been trying to explain. The appearance of the singularity just means that GR does not apply in that region (it can’t make physical predictions there), just as Maxwell’s equations don’t apply on quantum scales. No one in their right mind would take singularities as actual reality. As long as they are compatible with what has already been scientifically established, and so long as they are falsifiable - sure. In this case that means any proposal needs to be compatible with the laws of gravity, as well as with the already well tested and established parts of the Standard Model - I think your idea fails both of these criteria, for the reasons explained. So it really doesn’t matter what anyone says, because in the end it doesn’t make a difference to you? I have already shown you why it isn’t feasible, and I have even hinted at how it can be tested (gravitational wave signatures, motion of test particles), but you haven’t accepted that. My guess is that, even if I were to work through the entire maths from start to finish, you still wouldn’t accept it. And then - “If you don’t agree with my leading question, you are unscientific.” Ok. It seems I just wasted several hours of my time here, which I could have used better to work on my own GR-related projects - I gave you the benefit of the doubt, and thought you were genuine, so I wanted to help. My bad. And chances are this isn’t the first forum you’ve been posting this on, either - just my intuition. Good luck to you.

Leaving aside the actual collapse process itself, the end result of the collapse is simply a static ball of perfect exotic fluid, according to what you propose. The exterior vacuum of such an object is described by the AdS-Reissner-Nordström metric, as given earlier. This is a very different spacetime from Schwarzschild. The metric is a global property of the spacetime, so of course all the various regions depend on one another via boundary conditions. This has nothing to do with the propagation of information. My answer to this is a ‘no’, for all the reasons previously given. Yes, it does indeed. In pretty much the same way that singularities appear for point charges in Maxwell’s electrodynamics, or for the Big Bang in cosmology. But what does this actually mean? It means simply that for the process in question, the model that is being used has been extended beyond its domain of applicability (which is always limited for any model in physics). It does not mean that a point of infinite energy is being ‘predicted’ to physically exist. So, the appearance of the singularity in GR means that the end stages of a gravitational collapse process are outside the model’s domain of applicability - which should really go without saying, since it’s a purely classical model. You fix this by extending the model’s domain of applicability - you go from Maxwell’s ED to quantum electrodynamics for example, and for gravity we will need to go from GR to some as yet unknown model of quantum gravity. It makes little sense to attempt to hide the singularity by proposing some ad-hoc mechanism that has no physical basis; you can’t really fix a singularity from within a singular model. You can only hide it, which isn’t the same thing. As such, I see very little benefit or reason in what you are proposing, even if it did somehow work; it just introduces a whole new range of difficulties (whether you acknowledge those or not), without addressing the fact that the model itself goes singular in situations where quantum effects become non-negligible, which isn’t just during gravitational collapse. So to me, the way forward is to continue research into quantum gravity - not postulating things for which there is no theoretical or observational basis. Does this answer you question, even if you don’t agree with the answer?

Not the matter itself, but the metric of the spacetime. If there is exotic matter, the spacetime in which it lives has to have a non-vanishing cosmological constant - it needs to have the metric I gave earlier. I have explained this already. That’s exactly what I pointed out earlier - that test particles will fall away from the surface of a ball of exotic matter. That would be so in Schwarzschild with (-M), and also in AdS Reissner-Nordström. I didn’t say that it does. What I said was that the conversion process from ordinary matter to exotic matter is an issue, both for GR as well as within the Standard Model. And I said that the geometry of spacetime containing exotic matter isn’t just some kind of ‘inverted Schwarzschild metric’. A shrinking ball with constant total ordinary mass, so long as the situation is spherically symmetric, will have an exterior vacuum metric that is static and stationary (that’s just Schwarzschild), so Birkhoff’s theorem applies. However, what you propose is a process whereby M -> (-M), so Birkhoff does not apply in your case. This is consistent with the earlier finding that the exterior vacuum metric of a ball of exotic matter is not Schwarzschild (how could it be if ‘M’ varies?). BTW, did you consider what happens when, in your idea, the collapse reaches the point where you have equal amounts of exotic matter and ordinary matter, and net total mass=0? Right, at this point I’m going to ask you right out - are you actually interested in anyone else’s view on your idea? Or are you just here to try and prove yourself right, no matter what it takes? Because that’s the impression I am getting. And I’d really like an honest answer. I can’t speak for others here, but so far as I am concerned, if you have genuine questions, then I’m happy to help, but my answers will always be in the context of established physics; but if this is a “I’m right, try to prove me wrong” kind of situation, then I‘m sorry but I can’t help you. So what are you hoping to get out of this thread? And please be honest, because right now this is all going around in circles.

Ok, thanks! This can’t do what I need it to do, as far as I can see...but that’s ok, I’ll just have to sit down and do it by hand. It’ll take more time, but I’ll get there (eventually)

Well, then you need to start with an energy-momentum tensor that isn’t stationary (i.e. some or all of its components will be time-dependent); unfortunately then the resulting metric won’t be stationary either, so it won’t be Schwarzschild. So basically you want to start with ordinary matter (described by some non-stationary non-vacuum metric without cosmological constant), that somehow transforms into exotic matter (necessarily described by a metric with non-vanishing cosmological constant, as quoted above). Even without any further consideration, it is already clear that a process like this is incompatible with GR, because the cosmological constant is a conserved quantity - you can’t have it being zero in one region, and non-zero in another. No you don’t. The ‘M’ is a parameter in a 1-parameter family of metrics, it can’t be negative. It also can’t change from M to (-M), because it is a conserved quantity that is a property of the entire spacetime. If you propose any process where M varies in any way, then you are no longer in Schwarzschild spacetime (such spacetimes are of type Vaidya-Bonner). No, I am telling you two things: that such a process isn’t physically possible because it is in violation of both GR and the Standard Model; and that, if it were somehow possible, the exterior geometry couldn’t be Schwarzschild. It applies only to spacetimes that are vacuum in the exterior. If your fluid ball is embedded in a region of spacetime that isn’t a vacuum (e.g. Vaidya spacetime), then we are again dealing with a completely different situation, that requires detailed analysis.

I don’t have anything to run as such. I used to have a MAPLE installation, and in MAPLE there was a package where you just inputted the components of the metric tensor (in symbolic notation), and it would symbolically calculate the Christoffel symbols (as well as Ricci, Riemann, Einstein and Weyl tensors). I was just hoping that someone here might have access to MAPLE and thus a way to do this for me, since finding all the non-vanishing Christoffel symbols is tedious and quite frankly a pain in the backside. I have never used any other CAM software, so I’m not sure if this is possible with other applications also. It’s probably a long shot though

Your original post was about Schwarzschild spacetime, which is static and stationary. If you abandon those boundary conditions, then things are going to become very, very complicated very quickly. Gravitational waves have nothing to do with this (the spacetime is stationary!), and no information is being propagated - this isn’t the issue. The issue is rather that you can’t just glue arbitrary regions of spacetime together any which way you want - once you have a specific geometry in one region, then this places very stringent constraints on the kind of geometry adjacent regions can have, because spacetime needs to remain smooth and continuous at the boundary between the two, and the global metric (which covers both regions) has to itself be a valid solution to the field equations. In most cases, this uniquely fixes the entire geometry. In this case, if you have a ball of perfect exotic matter fluid, the exterior can only be an AdS-Reissner-Nordström metric, and nothing else. The exterior metric is the same whether the exotic matter fluid in the interior collapses, or not - same as in the Schwarzschild case. But it is not the same if you replace ordinary matter with exotic matter, because the two give rise to entirely different geometries (and topologies!). If you start with the energy-momentum tensor of a ball of perfect exotic matter fluid in a stationary spacetime, and insert it into the field equations, you obtain a single unique interior solution - because of smoothness and continuity boundary conditions, and because all metrics need to be valid solutions to the field equations, this automatically gives rise to a single unique solution for the exterior vacuum - being the metric I quoted. The same is true for Schwarzschild as well - the exterior (vacuum) Schwarzschild metric can only be coupled to an interior (ordinary matter) Schwarzschild metric, and nothing else. You don’t need to take my (or anyone else’s) word for this, you can work through the maths yourself, if you need further proof (but be warned, the maths aren’t trivial!). Start with the energy-momentum tensor given above, and see if you can derive the Schwarzschild metric from it. I’m afraid I fail to see the connection. WBG spacetimes exclusively arise from ordinary matter. I think there is a fundamental misunderstanding here - it seems you think that, just because exotic mass differs only by a sign in the energy-momentum tensor, the resulting exterior metric has to be of the same form as Schwarzschild. But that is not so, because the GR equations are highly non-linear; just flipping a sign in the input does not translate to just flipping a sign at the output. Instead, it leads to a completely different spacetime with a completely different geometry and topology - both in the interior and the exterior. That is the nature of coupled systems of non-linear partial differential equations. He’s referring to the exterior vacuum solution outside the fluid ball.

I have never heard of Octave, so not sure about this. As for MAPLE, my main work computer is an iPad Pro (I live off-grid on a 12V solar system), so this is not an option. I’m afraid I don’t have access to Mathematica either.

I am currently working on a GR related project, and I wonder if there is anyone here who has access to a MAPLE installation? I need help to save me lots of work with the following: suppose we have a GR spacetime endowed with the usual Levi-Civita connection and the metric \[ds^{2} =-\left( 1-\frac{2M( u)}{r}\right) du^{2} -2dudr+r^{2}\left( d\theta ^{2} +sin^{2} \theta d\phi ^{2}\right)\] wherein M(u) is an unspecified everywhere differentiable function. My task is now to find all non-vanishing Christoffel symbols (2nd kind) for this metric, in terms of the mass function M(u) and its derivatives. I could of course do this by hand with pen-and-paper, but this is tedious, time consuming, and error prone; MAPLE has a differential geometry module that can automate this task. Is there anyone here who might be able to run this through MAPLE for me, and post the Christoffel symbols? This would save me lots of work and time To give a wider context, I need the Christoffel symbols so that I can write down the geodesic equations, and solve them for a purely radial free fall from rest at infinity. The above metric describes the exterior of a Vaidya black hole; I know already that the in-fall time from infinity to horizon is finite and well defined (unlike in Schwarzschild spacetime), but I need to find an explicit expression for that in-fall time in terms of the mass function M(u). Thank you in advance

I suggest you should first of all check whether the concept you propose is mathematically consistent with basic laws of physics or not, before you even start to worry about observational evidence. I'll help you out a bit more - consider the energy-momentum tensor for an exotic matter perfect fluid distribution: \[T_{\mu \nu } =-|\rho |u_{\mu } v_{\nu }\] Assuming that this distribution is static, stationary, and spherically symmetric (same conditions as Schwarzschild), it can be shown (Mann 1997) that the only possible exterior vacuum metric that is consistent with the Einstein equations for this scenario has to have the form \[ds^{2} =-A( r,\Lambda ,M) dt^{2} +\frac{1}{A( r,\Lambda ,M)} dr^{2} +r^{2} d\Omega ^{2}\] with the coefficient function \[A( r,\Lambda ,M) =\left(\frac{1}{3} |\Lambda |r^{2} -1+\frac{2M}{r}\right)\] and \(\Lambda<0\). I reiterate again that this is the only possible solution to the Einstein equations which can be matched to a spherical ball of perfect exotic matter fluid - this can be formally proven using a generalised form of Birkhoff's theorem (Bronnikov/Kovalchuk 1980), or alternatively by directly solving the field equations (Mann 1997). It is immediately obvious that this is not a Schwarzschild spacetime - which is why I kept pointing out to you that a Schwarzschild vacuum cannot be glued to this type of energy-momentum distribution. This is actually a rather interesting metric, because it has a fairly complex geometry akin to a Reissner-Nordstroem anti-DeSitter spacetime; there are two event horizons (an inner and an outer one), it is not asymptotically flat, and the global topology is not trivial either. Note that neither one of the horizons is located at what would be the Schwarzschild radius in Schwarzschild spacetime. Because the geodesic structure of such a spacetime is very different from that of Schwarzschild, it would be easy to observationally distinguish the two. If you have the mathematical skills, you could use the above to start your own investigations. Essentially what I am saying to you is that the very idea of having a Schwarzschild vacuum exterior to a distribution of an exotic perfect fluid ball is not consistent with the basic laws of gravity - so the concept is not internally self-consistent, and can't work, irrespective of any finer details.

Energy conditions are not amongst the boundary conditions used to solve the field equations for the Schwarzschild metric. Yes, we are assuming that it works well up to the point when quantum corrections become non-negligible. How do you know this? Energy density/mass isn't the only source of gravity in the field equations. Since spacetime in and around the horizon is smooth and regular, no PT reversal can happen there. It is not an assumption of the paper, it is a finding - you can not glue a region of negative mass to one of positive mass, without violating basic laws of gravity, which is why the entire universe in the scenario is negative mass. And even if you could, black holes with singularities would still occur, as the author correctly points out, since mass isn't the only source of gravity. There is no such thing as a time transformation (I presume you mean time reversal) at the horizon. And if there were, then you actually had a big problem, because the Standard Model is not invariant under T or PT reversals. Yes, you can do this, but what I am trying to point out is that the exterior vacuum cannot have Schwarzschild geometry - it will be a different type of spacetime. The wave signature depends on the geometry of the entire spacetime, i.e. the overall metric. No. Two bodies composed of exotic matter must always fall away from each other, and their exterior vacuum isn't Schwarzschild. How could it be? The maximally extended Schwarzschild solution (including both the interior of the collapsing star as well as the external vacuum) arises from an energy-momentum tensor for regular matter; if you change this source term, you are going to get a different solution. The other thing is that the 'M' constant in the Schwarzschild metric is a parameter for a 1-parameter family of metrics - so it is a property of the entire spacetime. Ok. Energy conditions aren't really the problem here, in my opinion. The main issue is that you are postulating a whole range of things that are very difficult or impossible to reconcile with already known physics, and that you make a number of assumptions that you believe to be true, but haven't actually explicitly checked: 1. That there is a PT or T reversal at the horizon 2. That such a reversal somehow transforms ordinary matter into exotic matter 3. That exotic matter is compatible with the Standard Model 4. That a body made of exotic matter has exterior Schwarzschild geometry 5. That this process avoids the formation of a singularity In the conventional GR picture, we assume only that the classical model remains valid up to the point where quantum effects can no longer be neglected. To be honest, postulating exotic matter creates many more problems than it could possibly solve (and I don't believe it actually solves anything), so it's of not much value. Can I suggest you make an effort to put some maths around your idea, because without a mathematical framework you don't really have a model, you only have a collection of assumptions and conjectures. Once the maths are in place, things can be checked directly. There is a really fine line between asking for honest feedback on an idea, and (perhaps unconsciously) already being convinced that it must be right, and thus finding ways to 'prove' it. I've given you honest feedback (this is from someone who has been working with gravitational models - not just GR - for a long time), and it is up to yourself now what you do with that. My honest opinion is that what you suggest doesn't work, and even if it did, it wouldn't actually solve anything. I'll leave you to it.