Mordred

That would be a causality violation c is the speed limit of information exchange as well.

found it I finally recalled it was a series of Black star research "Irreversible gravitational collapse: black stars or black holes?" https://arxiv.org/abs/1105.3394 I certainly wouldn't argue with this. LOL I know any personal modelling I do I set Planck units as a constraint on anything involving spacetime or other fields. Funny thing is that boundary works well with the FLRW metric for the 10^{-43} second boundary the average estimated temp of 10^19 GeV when you convert is in the same orders of magnitude as Planck temperature. With the temperature scale factor relation. Blackbody temp can be estimated by the inverse of the scale factor. This also corresponds to 1 Planck length. just an interesting tidbit on last.

It was several peer reviewed article on Arxiv but it was a few years ago that I followed the research and some of the proposed tests. However I'll take a look and if I can find the papers. If I can I'll post it. Point of detail the singularity conditions regarding the EH involve infinite redshifts and subsequent time dilation relations involving the EH. These conditions are the ones directly involved with regards to Hawking radiation. This also involves Unruh radiation https://arxiv.org/abs/0710.5373

so you googled a bunch of answers so tell me google what happened to the mass of the collapsing star then.... can you answer that or did it simply disappear. That is directed at google not you lol . Would you like to see equations that directly relate to the density term in regards to the collapsing star? https://arxiv.org/pdf/2310.17647 see section 4 If Victor Toth stated that then he only looked at the vacuum solutions of the interior and ignored the coordinate assigned for the singularity R=0. Not surprising though most articles tend to ignore that part as no one feels the singularity condition should exist. I have another related article that suggests that the BH may simply be a neutron star that has collapsed just beyond its EH but is still present. As mentioned no one knows beyond the EH. So its really anyone's game until we can find a means of indirect evidence to give us more clues. Gravity waves is a viable possibility others are mentioned here. The article that has some suggestive tests via the accretion disk is here https://arxiv.org/pdf/1104.5499 there is also a section covering Hawking radiation. However one will be quite surprised at all the processes matter undergoes in that accretion disk. I recall years ago I asked my instructor " How can you possibly have infinite density or near infinite density" his answer was that although fermions cannot share the same space with the same state that restriction does not apply to bosons. " you can in fact have extremely high density and still be a vacuum solution with incredibly high temperature and density. Vacuum describes a pressure term. Its not the energy density. You get the energy density by the equations of state for the particles contained within a region. Its one thing that often confuses ppl concerning vacuum. It can be positive or negative and can describe any range of energy density. If you think about that you might consider that a star is simply a condensed matter field it can be equally treated as a field. We know in cosmology we get a similar phenomena due to the BB and its mass density terms. I didnt have time to properly respond to the quoted section earlier as I was at work. Having time now I can provide a better response. just to add the singularity at r=0 is a true singularity it cannot be removed by a change in metric choice. The event horizon itself is often described as a singularity condition however that is a coordinate singularity and not a true singularity. https://en.wikipedia.org/wiki/Kerr_metric "Rotating black holes have surfaces where the metric seems to have apparent singularities; the size and shape of these surfaces depends on the black hole's mass and angular momentum. The outer surface encloses the ergosphere and has a shape similar to a flattened sphere. The inner surface marks the event horizon; objects passing into the interior of this horizon can never again communicate with the world outside that horizon. However, neither surface is a true singularity, since their apparent singularity can be eliminated in a different coordinate system. A similar situation obtains when considering the Schwarzschild metric which also appears to result in a singularity at 𝑟=𝑟s dividing the space above and below rs into two disconnected patches; using a different coordinate transformation one can then relate the extended external patch to the inner patch (see Schwarzschild metric § Singularities and black holes) – such a coordinate transformation eliminates the apparent singularity where the inner and outer surfaces meet. Objects between these two surfaces must co-rotate with the rotating black hole, as noted above; this feature can in principle be used to extract energy from a rotating black hole, up to its invariant mass energy, Mc2." I suspect this is what Victor Toth was referring to hope that helps Mathius Balu has an excellent coverage of this http://www.blau.itp.unibe.ch/newlecturesGR.pdf He will use the BH to help explain: "artifacts of coordinate choice" I would have to dig through it though to relocate the relevant section lol and just to add flames to the proverbial fire. A rotating BH has more than one event horizon..... google is useful but unless your aware of other factors getting good answers can often mislead down the wrong google pathway. For example simply googling BH singularity will more likely than not describe the coordinate singularities regarding the EH rather than the R=0 singularity condition. This wiki has the relevant detail regarding the Gravitational singularity as the link describes it The case r = 0 is different, however. If one asks that the solution be valid for all r one runs into a true physical singularity, or gravitational singularity, at the origin. To see that this is a true singularity one must look at quantities that are independent of the choice of coordinates. One such important quantity is the Kretschmann invariant, which is given by 𝑅𝛼𝛽𝛾𝛿𝑅𝛼𝛽𝛾𝛿=12𝑟s2𝑟6=48𝐺2𝑀2𝑐4𝑟6. At r = 0 the curvature becomes infinite, indicating the presence of a singularity. At this point the metric cannot be extended in a smooth manner (the Kretschmann invariant involves second derivatives of the metric), spacetime itself is then no longer well-defined. Furthermore, Sbierski[21] showed the metric cannot be extended even in a continuous manner. For a long time it was thought that such a solution was non-physical. However, a greater understanding of general relativity led to the realization that such singularities were a generic feature of the theory and not just an exotic special case https://en.wikipedia.org/wiki/Schwarzschild_metric#Singularities_and_black_holes

How particles scatter, or form new particles etc etc always depends on their cross sections . That uses the Breit Wigner equations along with the Feymann golden rules. It not some case of a photon knowing anything. When it encounters another particle the cross sections and Feymann golden rules are used to determine the end results. Granted we also have a table that is helpful . https://en.m.wikipedia.org/wiki/Table_of_Clebsch–Gordan_coefficients

Not quite destructive interference you can have full annihilation if the two wavefunctions are equal but opposite its realistically no different between matter and antimatter colliding with its opposite. Think of all particles are field excitations under QFT. You can get full annihilation with matter why would photons as a boson be different the antiparticle is asymmetric to the photon. Keep in mind that doesn't apply to probability wavefunctions. You have to look at the creation/annihilation operators specifically for each using QFT. Course you could further consider baryogensesis and leptogenesis which we cannot explain as that also relates.

Correct its best to think of singularity as a point where the math used breaks down.

Vacuum can have an energy density ta da lol. That energy density can easily approach infinity keep in mind my original statement had "as close as possible " that allows a QM interpretation on Planck units for cutoff though Gravity has no effective UV cutoff for the mass term. That's a large part of why gravity isn't renormalizable. The IR cutoff is already established. For the record I've had numerous discussions with some mistakes he has made in other articles of his. Sometimes I'm correct other times he is just didn't explain something accurately enough with regards to Victor Toth. Cool character though he's friendly and easily talked to.

How so no one knows what goes o beyond the EH however the equations do lead to the infinite density singularity which everyone agrees is the issue regarding the singularity condition.

So inertial observers. By the way here's how to do the kissing number problem in four dimensions if your interested. THE KISSING NUMBER IN FOUR DIMENSIONS Oleg R. Musin "In three dimensions the problem was finally solved only in 1953 by Sch¨utte and van der Waerden. In this paper we present a solution of a long-standing problem about the kissing number in four dimensions. Namely, the equality k(4) = 24 is proved. The proof is based on a modification of Delsarte’s method." https://arxiv.org/pdf/math/0309430 you wish to use vectors well you have those relations here. Its rather detailed. as you linked Newton and the kissing number above thought you might find it handy with regards to your spheres

great so I employ full GR for an observer in each case which will get different answers ? Observers affect geometry. length contraction is part of SR. An observer moving at 90 % c won't see a circle. with the equivalence principle inertia has equivalence to gravity with regards to observer effects. Pythagorus theorem doesn't even work without conversions to restore Pythagorus theorem. So your triangles wouldn't work correctly. You do want your equation to be useful in some cosmology based measurements if the answer is yes then you will need to account for geometry changes. Your going to need to include the effects of curvature and observers in those coordinate changes.

precisely my point " its relative to the Observer. How do you define one observer from another ? How is it relative ? If I have an observer a coordinate \(c_1,x_1,y_1,z_1\) living in a gravity well. What effect does it have from an observer moving a 0.99 c etc etc. You have no means of describing one observer from any other observer. How do I know if you are using strictly Galilean relativity or Special relativity ? am I suppose to read your mind ?

gravitons are still a viable possibility you don't need them to describe a BH or the effects of Hawking radiation on a BH but its also not incorrect to do so. here is the thing about Hawking radiation a virtual particle pair must form outside the event horizon. Due to conservation laws all particles pop into existence as particle pairs primarily but not restricted to conservation of charge. (matter , antimatter for example) which Hawking radiation uses. the matter particle escapes to infinity while the antimatter particle falls in. Its a rather simplistic descriptive but the mass loss is due to being the anti particle of the pair. A photon is its own antiparticle. The difference between them isn't charge but rather its polarity. As a wave it obeys constructive and destructive interference. So anti-photons will annihilate with matter photons. Now this may or may not cause interference with other particles as all particles also have wave and particle like characteristics. However that is moot as the only thing needed is the antiparticle of the pair formed to fall into the BH regardless of what particle is involved. you would get a reduced mass through mass energy equivalence regardless if it is anti photons or some other particle type. As far s I know Hawking never did specify which particle was involved. His original paper simply had particle antiparticle pairs. As photons are generally used with blackbody radiation its the most common treatment. However you also have methods using entropy but entropy in particle physics related to effective degrees of freedom ie spin. charge , flavor, color, energy momentum etc. for example see here "Then Hawking’s black hole emission calculation [9, 10] for free fields gives the expected number of particles of the jth species with charge qj emitted in a wave mode labeled by frequency or energy ω, spheroidal harmonic l, axial quantum number or angular momentum m, and polarization or helicity p as Njωlmp = Γjωlmp{exp[2πκ−1 (ω − mΩ − qjΦ)] ∓ 1} −1 . (5) Here the upper sign (minus above) is for bosons, and the lower sign (plus above) is for fermions, and Γjωlmp is the absorption probability for an incoming wave of the mode being considered." https://arxiv.org/pdf/hep-th/0409024

I don't care what the title is. If your claiming you formula does this or that it requires the terms that relate to those claims.. Claiming redshift with no time component to describe frequencies is simply wrong old math or new math. Describing past and future gravity terms without anything relating to a force term is just as wrong. Claiming details concerning different observers without a coordinate system is another example. So far your equation only shows volume changes you need additional mathematics to do anything beyond that. This is the equation you posted does it describe anything at all beyond change in area ? The time component used in that equation would be observer dependent it's not proper time. proper time using a coordinate system is this for Euclidean geometry (flat spacetime) \[\Delta\tau=\sqrt{\Delta t^2-\frac{\Delta x^2}{c^2}-\frac{\Delta y^2}{c^2}-\frac{\Delta z^2}{c^2}}\] that's one of its simplest forms. The equation I posted only shows how to convert from coordinate time to proper time for 4d Spacetime using Cartesian coordinates it does nothing else... to have it do anything beyond that requires additional mathematics its as simple as that

You still require some term for rate of change as well as some terms regarding force for gravity etc. If your equation is now different than what you have posted so far you should include it. Though as I have already mentioned a uniform mass distribution has zero gravity as per Newtons Shell theorem. Even how we measure energy also depends on observer just as how one measures redshift depends on the observer. For that matter how measures volume can sometimes depend on observer a good example being the event horizon of a BH. Different observers will measure the event horizon at different volumes and radius. SR also teaches us that distance can also be observer dependent hence the length contraction of SR. I'm sure as an engineer your familiar with signal propagation caused by an EM field. Time dilation can readily relate to this as the coupling constants of the SM produces the mass term. Mass being resistance to inertia change. Just as I'm positive that you understand redshift involves frequencies which requires a rate aka time component.

We look into the past the further away we look. That's well established it's also why our equations use proper time and proper distance in its equations. The mathematics you've shown so far do not have any time dependency. You haven't got anything equating to a rate of change. Not from the equations you have so far posted and as how one measures time is relative to the observer you will need a GR treatment.

You have to understand that Hawking radiation is a thermodynamic process it's radiation equates to photons as the mediator for the EM spectrum which is used also for blackbody temperature. All equations involving blackbody temperature uses the photon as the mediator for its radiation terms. The other detail to recognize is that any object of any mass can be a blackhole if it's mass is contained in less than Schwarzschild radius. The Smaller the volume of the EH means the rate of Hawking radiation produced increases as the EH shrinks due to mass loss. The smaller the EH the greater the Hawking radiation. The singularity or as close to singularity as possible ie near infinite density would still have sufficient gravity as well as other related forces to maintain an EH even if that EH is smaller than a soccer ball etc.

At that range you wouldn't really need much deflection something as miniscule as a 1 degree defection would likely be sufficient if even that. Likely some form of craft that has sufficient mass to gravitationally causes a change in angle by using its thrusters to simply stay near the asteroid . One could also feasibly save fuel using solar sails to get there. At the mass of the asteroid tethering wouldn't be practical. Though the outgassing method is also viable. Those are the two methods I see as most viable out of the ones I'm aware of.

What you described above really doesn't make much sense sorry to say. Particularly in how your describing causality in regards to past and future events in regards to gravity. For starters there is no antigravity. Also if you have a uniform mass distribution according to Newtons Shell theorem.

Just to add to the good answers already posted. One hurdle to overcome is thinking of atoms in accordance to the Bohr model. Which modern physics knows to be incorrect. Instead the atom has a probability cloud with different configurations. All described via the Schrodinger equation. https://www.khanacademy.org/science/physics/quantum-physics/quantum-numbers-and-orbitals/a/the-quantum-mechanical-model-of-the-atom This article from Khan University has a decent coverage.

Theoretically viable it would depend on distance, asteroid size and composition.

Prior to the Higgs field dropping out of thermal equilibrium the universe would certainly have rapid expansion. Simply put all particles are in thermal equilibrium and massless. So their kinetic energy term for momentum certainly overpowered the potential energy terms from any fields present. Once the Higgs field drops out of thermal equilibrium and particles gain mass this definitely helps slow down the expansion. The slow roll stages of inflation corresponds to this. However not all particles drop out equilibrium at the same time even though the Higgs field has. They drop out a different times this can also be seen by the different particle generations of the SM model. For that matter even the Higgs field had stages of how it drops out of equilibrium. Every type of particle that drops out of equilibrium affects the expansion rate. So no Higgs was certainly not the last field to drop out of equilibrium. Any particle type can be treated as a separate field in a multiparticle state.

Simply put the way it's done in current modelling is multi body as per a field treatment. One main disadvantage you are having is not knowing just how flexible, interconnected between models physics really is today. For example using a very high particle count there have been some incredible simulations simply to test our theories and applying the formulas of mainstream physics. One of my favorite involved several supercomputers nearly a year if I recall but it is incredible in its detail. It tested not only large scale structure formation, it also tested metalicity,(Big Bang nucleosynthesis). Galaxy formation, etc. It's really worth watching and then realizing that it's applying the mainstream mathematics. This is an example of just how capable the way main stream physics does things mathematics truly is. One further detail there is no restrictions on what mathematical method one uses. You can integrals, derivatives whatever you choose. Physics will use any mathematical method provided it accurately describes the system or state. It prioritizes symmetry relations for invariance to all observers, independence of coordinate choice etc for very good reasons. A good way to learn these is gauge group theory. Just to give you some idea of just how detailed our models are mathematically. Truth of the matter is. If you can mathematically and accurately describe a given system or state etc. The method used isn't incorrect. It becomes a valid method. It may simply not be the most flexible method or may be too restrictive to what it can accurately describe.

Well the universe is expanding its why the equations I provided show the expansion with the energy density and pressure relations. The basic relation however being Hubbles law. The greater the distance the greater the recessive velocity. Key note this isn't a kinetic based velocity but rather an observer based velocity that depends on separation distance. \[v_r=H_O d\]

Your right I didn't bother responding to your logic. As I stated I lost interest. Particularly when you have statements such as information travelling faster than c that you cannot back up with any real physics or mathematics. This includes your holonomic toroid allowing a faster than c wave. This runs counter to well known and understood physics. So any logic based on this is meaningless if you cannot show how that's even possible under mathematics using known physics. Another example is some mysterious toroid travelling at c. It must be something massless to do that. However you can't describe it beyond your verbal claims. I also have no interest in downloading a paper from an outside source when the rules requires that material to presented here.. Who knows you might catch my interest once you start applying some real physics or mathematics. Rather than nothing more substantial than your logic