I think this is a pretty good question.

[Orion1]

In physics, there is a speculative notion that if there were a black hole with the same mass and charge as an electron, it would share many of the properties of the electron including the magnetic moment and Compton wavelength.

These equations define the electron as a single photon microgeon and also as a gravitationally confined particle with its gravitational force and electromagnetic force precisely balanced. It therefore has the properties of an extremal black hole without an event horizon.

The extremal black hole electron is clearly quantized, with only one mass value allowed, because gravitational force and electromagnetic force are required to be balanced.

A photon, confined by its self-gravitational attraction would have toroidal topology, as described in the paper, Is the electron a photon with toroidal topology? by J.G. Williamson and M.B. van der Mark. A gravitationally confined wave particle will have geon-like properties because its angular_momentum accounts for its total mass energy.

A dimensionless ratio that is equal to, 4 pi times 3Gm/c squared, divided by the electron Compton wavelength is (3/2) exponent 1/2, times Planck time, divided by 2 pi seconds.

Normally, the mass that we will able to measure in our frame of reference is the result of the gravitational force taking place in the black hole within time t0 and the rotational factor, which must be the same as the one used to get the electron charge. If we apply these conditions to Planck's mass m0, we have the electron mass me. This equation gives us the answer on the link between the very heavy particle m0 and the light electron mass. There is a time factor that we are unable to measure directly but it is an integral part of the electron mass.

If the gravitational force of mass m0 would exist only for the duration of time t0, we would have a gravitational force...

Again, we would not be able to measure time t0 and the ratio would look dimensionless.

I am having trouble getting dimensions to work out right. $$\hbar / c$$ has units of (Js)/(m/s) or Js2/m. Since a Joule is a kgm2/s2, then $$\hbar / c$$ has units of kg-m. G has units of m3/kgs2, so $$(\hbar / c)^3 / G$$ must have units (kgm)3 / (m3/kgs2), or kg4s2. So the mass of the electron you give doesn't have units of kg, but rather kg s1/2. Is there something missing somewhere?

According to the Journal of Theoretics, the black hole electron mass:
$$m_e = m_0 \sqrt{\frac{t_0 \alpha}{2}} = \text{kg} \cdot \text{s}^{\frac{1}{2}}$$
$$m_0$$ - Planck mass

According to Wikipedia, the black hole electron mass:
$$m_e = \left( \frac{h}{c} \right) \left( \frac{1}{4 \pi} \right) \left( \frac{c}{3 \pi h G} \left)^{\frac{1}{4}} = \text{kg} \cdot \text{s}^{\frac{1}{2}}$$

The issue that has been raised on Physics Forums is in regard to the Systeme International units of $$\text{kg} \cdot \text{s}^{\frac{1}{2}}$$, specifically the $$\text{s}^{\frac{1}{2}$$ with respect to particle mass.

The Wikipedia article in ref. 2, simply states that the 'directly unmeasurable' time dimension is actually Planck time and is divided by the dimension $$\boxed{dt = 1 \; \text{s}}$$, which results in a 'dimensionless ratio', which also raises an issue as to substantiation.

Unfortunately the scientific paper cited by Wikipedia and listed in ref. 3 for a black hole electron, is not legible in my Adobe Reader version. Is the black hole electron mass equation listed in this paper and is this paper pseudo-scientific?

Are these equations scientific or pseudo-scientific?

Reference:
http://www.journaloftheoretics.com/Articles/2-5/bh-dimario/dimario.htm#MASS"
http://en.wikipedia.org/wiki/Black_hole_electron#Discrete_Mass.2C_Spin_and_Stability"
http://members.chello.nl/~n.benschop/electron.pdf"

 

[cristo]

The Journal of Theoretics is a crackpot journal.

 

[alxm]

Sounds pretty crackpotty.

In physics, there is a speculative notion that if there were a black hole with the same mass and charge as an electron, it would share many of the properties of the electron including the magnetic moment and Compton wavelength.

Well obviously something defined so that it shares some properties of the electron will share other properties of the electron.

But the magnetic moment? I've never derived it, but I always assumed it was a property of the electron's spin. (Reasoning along that if it has 'intrinsic' angular momentum and a charge then it should have an 'intrinsic' magnetic moment) How could something with the same charge and different spin (are black holes bosons or fermions? ;) ) possibly give rise to the same magnetic moment? Is this even theoretically possible?