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Thread: A Look Into A Theoretical Stable Black Hole

  1. #1
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    A Look Into A Theoretical Stable Black Hole

    This work came independent of my last investigation, into the ''Holeum'' (which is a theoretically stable bound black hole pair which radiates gravitational waves) however, keep this in mind because when we come to look at this, we will find my model is not so far from the truth for the Holeum model as well. Instead of a gravitationally bound pair of black holes (which have been stated to be analogous to the hydrogen atom in the ground state), I too looked into a possibility drawn up by Motz, who considered a fundamental black hole system also in its ground state - and so incapable of giving off radiation - this postulate depends on a class of fundamental particle which it cannot decay into anything more simpler.

    First of all, what is actually special about these so-called Planck units?

    Hierarchy Problem And The Gravitational Charge

    In natural units,of the gravitational fine structure constant is equal to the square of the mass of a particle



    And the quantization of a mass depends on:



    The hope or immediate realization of this are attempts to find quantization of mass depending on factors of . The can be thought of as the gravitational charge of the system analogous to the electric charge . If we define the Rydberg constant in terms of the gravitational coupling constant we get:



    Even though the Rydberg constant was first applied to hydrogen atoms, it could be derived from fundamental concepts (according to Bohr). In which case we may hypothesize energy levels:



    Plugging in the last expressions we get an energy equation:



    The relativistic gamma appears from the definition of the deBroglie wavelength [1] and it suggests a relationship between Einstein's relativistic mass and the gravitational charge. It makes sense that the relativistic implication arises that the gravitational charge varies with the motion of the system since Einstein himself has shown that the mass of a system depends on its energy content. Increasing velocities imposes increasing relativistic energy, mass becomes more massive: this is just another way to say its gravitational charge becomes large. One thing that the equation does not do is predict the mass for particles. All it states is that the thing we call mass appears to vary with kinetic energy. Some mass formula have been suggested in literature (see ‘’What is special about the Planck mass?’’ Sivaram & Arun). Let’s have a quick look at a mass formula candidate suggested from the earliest mention I can track by Lloyd Motz:



    Or simply





    Immediately we can notice the use of the gravitational charge in the last term - the only difference is that it has focused on the Planck mass definition of the charge. The Planck mass should not necessarily be considered fundamental, it seems like too much a basic unit of matter for any particles we have observed in the standard model. Though the middle term is good for string dynamics and superstring tension, the last term appears to be made of more fundamental assumptions which included the gravitational charge of the system. The adjustable parameters is what allows us to predict particle masses and remains a curiosity that the formula is capable of predicting a wide range of particles on the standard model.

    [1] - The deBroglie relationship used was:



    The Entropy of a Black Hole Particle


    The idea of entropy existing for a particle incapable radiating any more energy, creates a problem in the issue of the temperature of the system in regards to the third law of thermodynamics. A question that remains is whether a micro black hole undergoes thermodynamic properties or whether it is highly unstable like we would expect for a small black hole.

    The radiation from a black hole is the sum of many discrete quantum processes, each one of which represents a single quantum transition from a higher to a lower quantum state. As Loyd Motz makes clear in his ''gravitational charge as a unifying principle,'' just like how the radiation from an atom will cease when every electron in the atom is in its lowest quantum state. Consequently, this would be the lowest quantum state for a gravitationally bound system.

    Using the Berkenstein entropy for the black hole can be written as



    In which A is the area of the black hole. There are additional arguments you can make for the black hole entropy and can be given as



    (Also see Motz in reference). If we define the Rydberg constant in terms of the gravitational coupling constant we get:



    Even though the Rydberg constant was first applied to hydrogen atoms, it could be derived from fundamental concepts (according to Bohr). In which case we may hypothesize energy levels:



    Plugging in the last expressions we get an energy equation:



    to be cont. next page
    Last edited by Dubbelosix; 2018-Jun-01 at 03:32 PM.

  2. #2
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    In fact, I wondered immediately if there are applications of this with the micro black hole and maybe in regards to its energy levels. We start with the equation



    Where the entropy has taken on the dimensions of the Boltzmann Constant. If you plug in the mass for a black hole:



    You will retrieve the Bekenstein entropy. It is often said that entropy has dimensions of the Boltzmann constant but it's entirely plausible, even with better arguments for, a dimensionless case of entropy in the form



    In which case, it is possible to identify the entropy in a dimensionless form



    In which the wave number is identified with the deBroglie wavelength



    For a black hole system however, when you introduce the appropriate smearing of quantum effects in the thermal wavelength definition, you can end up with new kinds of questions about what goes on inside of the black hole. In one case, a gas obeying Bose Einstein statistics or Fermi statistics is governed by the condition and so follow the rules of quantum mechanics, on the basis that the interparticle distance is smaller than the deBroglie thermal wavelength



    when the interparticle distance is much larger than the thermal de Broglie wavelength then it will follow the classical Boltzmann statistics



    The dependence of those conditions are more clear when written out:



    Where is the energy per particle. It may be considered strange to wonder whether the interior of a black hole might permit the physics of a condensate. The conventional view of a black hole, is that very small black holes are extremely hot compared to their larger cousins. A black hole in the ground state is not allowed to radiate electromagnetic energy, so what happens to the definition of temperature? These are interesting questions I would like to take up in another thread. For now, let's just cover one last thing concerning the Transition equation. We showed, it could be written in terms of the Boltzmann constant



    And this can decribe a black hole system in theory because the Bolztmann constant can be constructed entirely from Planck units.








    Of course this is a hypothesis: First it is a hypothesis of Motz that a black hole system follows the ordinary rules we associate to the energy levels of an atom – or even if they are at least analogous. The issue is we actually have no idea what goes on behind the event horizon of a black hole, but rest assured, Motz has at least offered a suggestion to a way forward at least in the realm of quantum mechanics. Then if his hypothesis is true, then it may be a logical move to find relationships to the usual transition equation featured above. The model proposed by Motz states that the black hole particle stops acting like a black body radiator in its lowest quantum state (keep in mind, black holes are generally considered ‘’near perfect’’ black body radiators). A consequence of black holes as near-perfect black bodies is that they cannot absorb photons with wavelength exceeding the black hole's size. This must also hold true for the Planck particle.

    Another way to look at this may be understood from Sivaram and Arun who calculate the interior of the black hole horizon in an approach using holography as a phase space consisting of filled with just one photon (or quantum action).



    In this limit we reach the Motz hypothesis suggesting a bound system which consists of a single quantum of action



    **References:**

    Matter wave - Wikipedia (https://en.wikipedia.org/wiki/Matter_wave)

    https://arxiv.org/ftp/arxiv/papers/0707/0707.0058.pdf (https://arxiv.org/ftp/arxiv/papers/0707/0707.0058.pdf)

    http://sci-hub.tw/10.1007/BF02822327 (http://sci-hub.tw/10.1007/BF02822327)

    http://inspirehep.net/record/6929?ln=en (http://inspirehep.net/record/6929?ln=en)

    https://www.researchgate.net/publica...k_Hole_Entropy

    https://arxiv.org/pdf/1306.0533.pdf (https://arxiv.org/pdf/1306.0533.pdf)

    https://arxiv.org/abs/1604.02589 (https://arxiv.org/abs/1604.02589)

    https://arxiv.org/abs/1005.3035 (https://arxiv.org/abs/1005.3035)

    http://www.preposterousuniverse.com/...tum-mechanics/

    (http://www.preposterousuniverse.com/...tum-mechanics/)

    (extra added) - for black holes possibly having an origin with Bose-Einstein condensates:

    Is the black hole at our galaxy’s centre a quantum computer? – Sabine Hossenfelder | Aeon Essays (https://aeon.co/essays/is-the-black-...antum-computer)

    Single-atom-resolved fluorescence imaging of an atomic Mott insulator (https://www.quantum-munich.de/media/...ott-insulator/)

    Astrophysics: Fire in the hole! (https://www.nature.com/news/astrophy...e-hole-1.12726)
    Last edited by Dubbelosix; 2018-Jun-01 at 03:57 PM.

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    On the Temperature-Entropy Problem for Micro Black Holes

    Black holes, even the microscopic kind, cannot be mathematically ruled out from physics - and if the work of Hawking is to be taken seriously, including analysis provided by Motz, then a black hole system really is deduced from a discrete set of quantum processes - those discrete processes always lead to an increase in the entropy of a system like a black hole .I have taken this recently to mean, that even a Planck particle (aka. black hole particles, or the Uniton as Motz named them) also must increase in entropy. How you actually interpret this with a particle with an infinite lifetime like a hypothetical class of particle black holes, is actually uncertain. We cannot of course rule out that entropic phenomenon take place in an increasing fashion since the third law of thermodynamics insists that the entropy of a system is only zero when the temperature is zero - we know this cannot ever be the case in science, since a zero temperature would correspond to zero motion inside the field. It’s an interesting question what happens to entropy in the ground state of a black hole particle since it has been shown the overall entropy of a black hole cannot decrease… only increase in time.

    The earliest model of a black hole stated that the entropy of a black hole was exactly zero - Hawking challenged this and stated if it has an entropy, then a black hole must possess a temperature and later we came to understand it as a thermal property of the black body radiation of the black hole. It may still be true, at least for the ground state black hole, that entropy may be essentially constant. When I read the model of Motz (leading me to investigate a black hole transition equation) he believed his ''Uniton'' had a temperature, but he did not specify the problems I have drawn up above. If a black hole system, any kind of black hole system, has a temperature, then it has a non-zero entropy and will radiate!

    So how can we have an increasing entropy but a system with an infinite lifetime?

    Something needs to give. The intuitive answer is that somewhere in the ground state, our usual understanding of entropy must break down. Entropy is a measure of disorder, and if a system is infinitely stable, then the disorder remains a constant. It could be that the black hole particle at near zero temperatures exhibits a behaviour like a zeno effect. The zeno effect is when an atom is incapable of giving off energy suspended in an otherwise, infinite animation and it will remain in a ground state because its wave function is incapable of evolving from the ground state. It is therefore similar to how an atom, ready to give up energy can be suspended infinitely in time - and the reason why it cannot give up radiation is essentially the same for the micro black hole, since the zeno effect is all about keeping an atom in the ground state. To put in a summary for clarity I have came to some conclusions but they may adapt in time:

    1. The Black Hole entropy rule dictating it always increases may apply only to macroscopic black holes and in the ground state will remain a constant.

    2. A ground state black hole has stability owed to it from two phenomenon: There is no fundamental particle it can decay into, coupled with a mechanism brought on about by a zeno effect (which halts the wave function evolution).

    The last conclusion here appeared to be a possible physics would could answer why a black hole with a temperature, may not be allowed to give its energy up, because something is affecting the systems wave function keeping it in the ground state. It would be interesting to see in the future, what kinds of physics might do this for the black hole.

  4. #4
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    This will be the last page for now, it finally gets to why my approach is similar to the Holeum model. And there is also the energy described as the Holeum energy is





    Our transition equation was formed from a modified version of the Rydberg constant,



    and as you can see, this is only one such factor of the fine structure off



    So the two theories are not too far apart - the thing we learn though it seems related to the Rydberg constant either way. The Hartree energy is twice the Rydberg energy .
    Last edited by Dubbelosix; 2018-Jun-01 at 05:48 PM.

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