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