Talk:Black hole electron

Planck length/ Compton wavelength
A clear size relationship is specified by an equation that compares length values as shown below. The length labeled (L2) is defined as 1/2 of the electron Compton wavelength. The value used for the Planck length is 1.616x10 exp-35 meters.

(L2)squared=(L3)(2pi)(Planck length)(3/2)exponent 1/2

When this equation is solved for (L3) the value found is 1.1835x10 exp 10 meters. This is a unique value because it is the wavelength of a photon that has energy equal to the Planck constant divided by the constant (2pi) squared. The implied value for the Planck length is 1.6159455x10 exp-35. I believe this relationship will become useful as the Bh electron article is filled in with information from other contributors.DonJStevens 15:43, 20 August 2006 (UTC)

The reader will note that the constant value h/(2pi)squared is directly related to fundamental features of the natural world just as h/2pi and h are related to fundamental features of the natural world.DonJStevens (talk) 13:34, 27 April 2009 (UTC)

The (L3) value is extremely close to the wavelength of a photon that has the energy value h divided by (2pi) squared. When the implied value for the Planck length is 1.6159455x10 exp-35, the implied value for the gravitational constant is 6.6717456x10 exp-11. It is an interesting surprise to find that the G value implied by electron properties is close to and even overlapped by G values that have been previously determined from laboratory measurements.DonJStevens 17:37, 16 September 2006 (UTC)


 * Don, I'm not sure I entirely follow what you're trying to do here. You've defined
 * $$L_3 = \frac{1}{8 \pi} \cdot \left(\frac{2}{3}\right)^\frac{1}{2} \cdot \frac{\lambda_{e}^2}{l_P}$$
 * and then you say that this is very close to "the wavelength of a photon that has the energy value h divided by (2pi) squared". But h has the dimensions of action (energy &times; time).  How are you getting from h to a photon energy?  -- Jheald 17:09, 21 September 2006 (UTC).

Answer; The L3 equation as you have written it is correct. The numerical value for L3 is 1.1834933x10 exp 10 meters when the Planck length value is 1.616x10 exp -35 meters. The L3 value found is very close to one light second (or 2.9979246x10 exp 8 meters) multiplied by the constant (2pi) squared. A photon with wavelength equal to one light second (and frequency of one cycle per second) will have (E=h times one cycle /sec) while a photon with the wavelength (2pi) squared times one light second will have [E=h times (1/2pi) squared cycle /sec]. It is correct to say L3 is approximately equal to (2pi) squared times one light second however rotating black hole properties imply that L3 should be precisely equal to (2pi) squared times one light second.DonJStevens 14:43, 22 September 2006 (UTC)

More facts; The approximate electron Schwarzschild radius can be specified as shown. The Le value is the electron Compton wavelength.

rs = 2/3 (Le/4pi)(Le/2L3) squared

With L3 equal to (2pi) squared times one light second, the radius is 1.3524368x10 exp-57 meter. This is approximately equal to the well known value 2Gm/c squared. The approximate radius and the well known radius values will be numerically equal when the implied G value (6.6717456x10 exp-11) is used. The two radius values are approximately equal when any of the (other) published G values is used.

The following equations can be easily verified to be approximately correct. They will be numerically correct when the implied G value is used.

3Gm/c squared = (Le/4pi)(Le/2L3) squared

m = (c squared/3G)(Le/4pi)(Le/2L3) squared

m = (1/3G)(Le/4pi) cubed, times (1/2pi) squared

m c squared = (c exp 4)(1/3G)(Le/4pi)(Le/2L3) squared

hc/Le = (c exp 4)(1/3G)(Le/4pi)(Le/2L3) squared

m = (h/4pi c)(c/3pi hG) exponent 1/4

The values h and G are shown to be closely related. The applicable G value is defined as shown.

G = (Le/4pi)^3 (1/2pi)^2 (1/3m) DonJStevens 16:24, 17 October 2006 (UTC)

Superfluid 3He
I'm reverting the most recent edit by User:Quasarq again:
 * 1) Micro black hole is already linked
 * 2) superfluid 3He stuff:
 * 3) It's not written well
 * 4) It's original research (reference to primary sources, I'm going to check out the SA article)
 * 5) It doesn't follow WP:MoS
 * 6) unification: M-Theory claims unification. M-Theory is unverified, but is definitely (not really arguable) adequate. Also, non-"M-theory" string theory also has a good explanation of unification (I'm not familiar with loop quantum gravity), so unless you're willing to list all the exceptions (which I can't say how many there are), it should remain closer to how it is.

It should be noted that I'm not opposed to this content in general, but it's going to have to be incorporated better. McKay 23:10, 13 September 2006 (UTC)

I read the relevant article in Scientific American. Black hole analogies, are merely that -- analogies of black holes. They are not black hole electrons with a new name. They do not belong in this article. For more information see User_talk:Quasarq. McKay 04:25, 14 September 2006 (UTC)

Binary Black Holes Needed

This page looks pretty good now, do we still need it? X [' Mac Davis '] ( SUPERDESK | Help me improve ) 07:47, 24 October 2006 (UTC)

Page still needs a link to article about theory of merging/colliding of black holes into one. Theoretically it is impossible for one black hole to press mass in its event horizon below the event horizon of another black hole. It is almost as difficult to lift mass back out of an event horizon at least in significant quantity. So offhand I would say two black holes merge extremely slowly due to relativistic effects at their event horizons and only at the point of contact between event horizons. Remember all new mass becomes frozen in relativistic time at the event horizon and black holes grow onion layer wise as the event horizon increases. So if an "object" if stops moving with respect to the event horizon surface...exactly how can two black holes deform geometrically to become one? Can the event horizon change shape increasing the area of contact? It initially appears that they might bounce into mutual orbit and eventually cluster cheek to cheek welded on position by gravity without merging for galactic eons. If one or both are rotating I can see how thin layers of mass would "adhere" to and rub off on to the larger black hole at the point of contact. On the other hand what happens to mass now inside the event horizon due to growth of the black hole? Apparently it still exists in some way as reflected by the gravity field. But maybe it is free to shift about inside at speeds above the speed of light - after all they call it a singularity in the mathematics of space-time. Is this an instantaneous macroscopic quantum event? Damn think of the gravity waves as the two separate centers of mass (potentially kilometers apart for stellar sized black holes) displace to be one. Gulp think of the gravity waves for two merging galactic black holes!!! Can you say life sterilizing event for much of the local universe - at least that galactic cluster? Or is the eventual merger an end of the universe type event where the black holes do deform but ever so gradually? 69.23.124.142 (talk) 08:02, 7 February 2009 (UTC)

Reply. See article "Naked Singularities",Scientific American, February, 2009, by Pankaj S. Joshi. Quote: "Charging up a black hole is harder because a charged hole repels particles of the same charge and draws in oppositely charged ones. -- Researchers continue to debate whether the black hole would eventually save itself or would crack open --." -- "Because general relativity breaks down at singularities, it cannot predict what those singularities will do."DonJStevens (talk) 16:31, 8 February 2009 (UTC)]]

Reply 2. Overview at Binary black hole. Studying the coalescence of astrophysical black holes is done under the moniker CBC "compact binary collisions" (since analysis when one or both of the partners is, say, a neutron star, is quite similar.) For recent sources see references discussed on p2 of https://arxiv.org/pdf/gr-qc/9602024.pdf. At present (2020,) likely long after your posting, LIGO has observed many of these events.

As they observed, black holes do not take forever to get together. Once two black holes, the kind you're familiar with (without charge or extremal spin,) are "close enough," the system will start losing energy like crazy by radiating gravitational waves, and the two objects will spiral toward each other. One reason the infinitely-long scenario you suggest does not happen is that their event horizons are still quite far apart when the two black holes coalesce and become one. Roughly speaking, this starts when their photon spheres touch. This last phase, known as "ring down," irons out any bumps in the structure and is very rapid.

Because astrophysical black holes with large, but not 'extremal,' spin have been observed, such as MAXI J1535-571, CBC calculations for them, as well as even for hypothetical "charged compact binary collisions" (cCBC,) which involve one or more charged objects, have been studied.

But the hypothetical black hole electron discussed in the current article has so much charge and spin relative to its invariant mass that it would have a naked singularity - that is, one unshielded by any event horizon. You would not need to worry about a second object taking forever to get to its event horizon ... there is none.

Matter-wave quantum
The electron mass energy is related to a specific photon wavelength so its mass energy is related to the Planck constant. In the book "The Enigmatic Electron", by Malcolm MacGregor (page 25) the electron is referred to as "the discrete quantum of matter-wave systems". Later (page 67) the author suggests that electron properties may be a guide to bridge the quantum and classical domains. From the electron mass and light velocity, a relationship between the (quantum) Planck constant and the (classical) gravitational constant is specified.

Le = 2(3Gm)exp 1/3, times (2pi)exp 5/3

h/2mc = (3Gm)exp 1/3, times (2pi)exp 5/3

h = 2mc(3Gm)exp 1/3, times (2pi)exp 5/3

This provides a partial bridge between the two domains.

DonJStevens 19:33, 3 January 2007 (UTC)

Stability / Infinite density
When an electron is infinitely small, its electric field will be infinitely large. In his book "The Quantum World", author Kenneth Ford writes, "Physicists will be happy if the things we call particles and that seem to exist at points are eventually shown to occupy some region - albeit an incredibly small region - of space" (page 241).

Theorists are not satisfied with words like infinitely small and infinitely large to describe electron properties. It is known that negative electric charge elements repel one another so that a significant force is required to hold the electron together. No combination of electric and magnetic forces has been proposed that can produce a stable state. Author, Malcolm MacGregor noted that gravitational forces could solve the stability problem if the electron is incredibly small. See book, "The Enigmatic Electron" page 72. The density required for stability is clearly achieved before the electron radius is reduced to zero meters (a point). The electron must occupy a small region of space so that its electric field and density are not required to be infinitely large.

DonJStevens 18:58, 19 January 2007 (UTC) DonJStevens 15:58, 3 February 2007 (UTC)

Not infinitely large as in area. You meant its field strength would be required to be infinitely intense/large. However there is no reason that the volume occupied by elementary particles needs to fall into the range measurable by photonic energy. That would mean finite but unmeasurable size...unless we find a different force/spectrum to measure with. How about gravity? Have we quantized it into Heisenberg terms yet? Oh rats we have indirectly. All mass is composed of oodles of quantum states and thus varying mass...except potentially stable Planck sized black holes which are basically undetectable themselves. 69.23.124.142 (talk) 08:04, 7 February 2009 (UTC)

super-extremal?
A black hole must satisfy |Q| ≤ M for there to be an event horizon, while |Q_e| >> M_e. Without an event horizon, how can an object meaningfully be termed a black hole? —The preceding unsigned comment was added by 209.250.133.53 (talk) 17:40, 17 February 2007 (UTC).


 * Hmm, I made reference to a problem with the page you referenced. Take a look at the talk page. But if I understand you correctly, it's actually the whole point behind this article. McKay 01:37, 18 February 2007 (UTC)

Added reply: The Russian physicist, Alexander Burinskii describes the Kerr-Newman black hole electron as a particle without a horizon. In his paper "The Dirac-Kerr electron" he writes (page 2) "Recall, that angular momentum J=h bar/2 for parameters of electron is so high that black hole horizons disappear and the source of the spinning particle represents a naked singular ring". DonJStevens 18:02, 18 February 2007 (UTC)


 * Wow, I think that's just a tad bit over my head. I guess I'm not sure how that applies to a comparison of Charge and Mass? McKay 05:09, 19 February 2007 (UTC)

Improved reply: The charge and mass comparison discussion should begin with relationships that all can agree on. The electron charge energy (electric field plus magnetic field) will be equal to the electron mass energy and this energy will be equal to 1/2 of the energy of a photon with wavelength 1.213x10 exp-12 meters (approx). This wavelength photon will have the energy density to convert to a pair of black hole particles when subjected to appropriate gravitational blue shift (time dilation) and an equal amount of gravitational space contraction. If this wavelength photon is absorbed by a black hole, its electromagnetic energy becomes mass. If the black hole is unstable after absorption, it may emit a pair of electron mass particles. Each mass particle will have a size closely related to its Schwarzschild radius value. In order to be extremal and stable, the electron must have the minimum energy required for it to be confined by its own gravitational field. DonJStevens 18:09, 19 February 2007 (UTC)


 * Ahh, so we're comparing the energy of the charge and the energy of the mass, if so, then you've basically determined that the electron is the basis for comparison, then saying that the electron is a denerate case of the black hole because q=m doesn't really say much. Where did the comparisons of Q and M come from? McKay 04:36, 20 February 2007 (UTC)


 * Be careful here: There are three parameters to consider here:  mass, charge, and angular momentum (actually angular momentum per unit mass).  The last one is usually represented by a.  For the case of $$m^2 > q^2 + a^2$$, the Kerr-Newman horizins do vanish.  To compare all three, geometrized units are used where c=G=1.  More specifically, $$m = MG/c^2$$, $$q = Q\sqrt{G k_c}/c^2$$ (in cgs units), and $$a = A/c$$, where the capital letters are in "normal" units and the small letters are in geometrized units.  Note that all geometrized units are lengths.  I regret that I don't have the time to do the calculations for an electron right now. --EMS | Talk 06:18, 20 February 2007 (UTC)


 * The electron mass and the electromagnetic energy released during particle annihilation are "given" values that require explanation. The dimensionless ratio (electron Compton wavelength) divided by 4pi(3Gm/c squared) is required to be a function of the gravitational potential at the radius 3Gm/c squared. When this ratio is explained we will be close to explaining why the electron mass is quantized. DonJStevens 16:33, 20 February 2007 (UTC)


 * Okay, I can help with the calculations for an electron. For an electron:
 * m = 6.76345536e-58 meters
 * q = 1.38057828e-36 meters
 * a = ...
 * I can't quite get the units to work out right. you say it should be a = A / c, but A is in units of J * s, or kg * m^2 / s. Dividing by c gives us units in kg * m, which gets us off by a factor of kilograms, the conversion to eliminate the kilograms (G/c2), results in a units of m2 which is also wrong, can I just take the square root? That doesn't quite seem right, I'm not sure. In any case, what I got was 3.04639314e-43 m kg.
 * Where do we go from here? I still don't feel right about applying "$$m^2 > q^2 + a^2$$" because my units aren't right yet. McKay 16:44, 20 February 2007 (UTC)

Angular momentum has geometric dimension of area. Angular momentum per unit mass will be meters.DonJStevens 18:52, 21 February 2007 (UTC)
 * Ahh, I missed the parenthetical remark "(actually angular momentum per unit mass)" so, the numbers are:
 * m = 6.76345536e-58 meters
 * q = 1.38057828e-36 meters
 * a = 3.34423694e-13 meters
 * For this case, the mass is much smaller than the combined charge and angular momentum (when geometrized with G and c), so there isn't an event horizon (according to this metric). Perhaps this should be incorporated into the article? McKay 19:42, 21 February 2007 (UTC)


 * I'm glad that you figured out the per-unit-mass business. Sorry that I was not around to help earlier with that.  As for incorporating this into the article:  I would first double-check the numbers, but if they are right the next issue may be seeking a reliable source for this.  This looks like something that should be known, but without a source I cannot vouch that it is.  (BTW, the m and q values do look right to me, but I have never computed a before.) --EMS | Talk 05:32, 22 February 2007 (UTC)
 * Yeah, we can't add it until we have a source. I'm merely adding information to (and learning about :) ) a claim that someone made on the talk page. It does appear as if the claim has merit, I would imagine that the person who made the intial edit (User:209.250.133.53) might have a source, Feel free to check my work. I could have made a mistake. I feel confident about my work, it was done on google calculator. I usually use units to check my work, and they came out clean. Feel free to check it, errors could be anywhere.McKay 06:02, 22 February 2007 (UTC)


 * I don't doubt your math and have fewer doubts on the conclusion. I have run across the electron being super-extremal before.  My only concern here is the integrity of the encyclopedia, but even then I see this as an important and relevant finding which almost certainly has been noticed before.  Perhaps using the fact template may be sufficient to permit the inclusion of this interesting finding in the article.  At the least, this is not a controverial finding for those of us who are familiar with GR and see the math. --EMS | Talk 15:54, 22 February 2007 (UTC)

I need a math check so we can all be on the same page. I have angular momentum value (h/4pi)(G/c cubed) or 1.306x10exp -70. This value divided by 6.763x10exp -58 is 1.931x10exp -13. The "a" value would then be close to 1.931x10exp -13 meters unless I missed something. Let me know if I made an error. DonJStevens 18:16, 23 February 2007 (UTC)
 * Hmm, at first, I thought your units were messed up, but they're not.
 * So I reduced yours to elminate duplicates, and only then did I check that it was off by a factor of two. hbar is h/2pi, not h/4pi. so I think my original number is correct.
 * For my result:Check this out Google calculator McKay 05:11, 24 February 2007 (UTC)


 * Hi McKay. Thanks for the math check. In any case the horizons appear to vanish. This is significant. DonJStevens 15:12, 24 February 2007 (UTC)
 * The reader will note that the (m) value found, 6.763x10 exp-58 meters is equal to the radius (L2/2pi) meters (or 1.931x10 exp-13 meters) multiplied by the time dilation ratio (L1/L2) squared and also multiplied by the fraction (1/3). Values obtained will be numerically consistant when the implied G value is used. This will require further evaluation.DonJStevens 18:34, 10 May 2007 (UTC)
 * For the electron, (m) squared is not greater than (a) squared. Centrifugal forces are expected to halt the collapse before a Schwarzschild radius size is reached, so it is misleading to call the electron a black hole without further explanation. Like a black hole it has the energy density needed for gravitational confinement and like a geon, it is a gravitationally confined wave. A better name is needed. DonJStevens (talk) 16:02, 21 March 2008 (UTC)

Source; m squared requirement
In his book "The Road To Reality" page 832, Roger Penrose writes, regarding electrons and the K-N gyromagnetic ratio 2,"It could only apply if an electron could be regarded as being, in some sense a black hole". He then notes that the electron does not meet the requirement that (m)exp 2 must be equal to or greater than (a)exp 2 plus (e)exp 2 in order that the "--Kerr-Newman metric can represent a black hole".

Many theorists agree however, with the statement by Chris Isham; "One of the major predictions of Einstein's theory is the phenomenon of gravitational collapse in which ---, matter that is compressed to more than a critical density will inevitably collapse under its self-gravitational attraction until it becomes a --- gravitational singularity".

The critical density is clearly reached before the electron radius is reduced to a point. DonJStevens 17:25, 5 March 2007 (UTC)

Regarding the problem of cosmic censorship, Roger Penrose has noted that "cosmic censorship" is a mathematical conjecture that is " -- as yet neither proved or refuted -- concerning general solutions of the Einstein equation". See pages 768 and 769 in his book "The Road To Reality". DonJStevens 18:41, 10 March 2007 (UTC)

Many readers will agree that the electron is, in some sense a black hole particle if it has the (black hole) mass density required for gravitational confinement. Theorist A. Burinskii included a "naked singular ring" in his electron particle description. The absence of horizons was expected by Burinskii however, this is in the realm of quantum gravity, about which little is known. Theory predicts there is a maximum angular momentum that a black hole of a given mass can have. The electron will have the maximum value (h/4pi). When the electron is analyzed as a thin ring its angular momentum defines a ring radius.

h/4pi = mcr

h/4pi mc = r = 1.9307963x10exp -13 meter

This radius value will have a ring circumference equal to 1/2 of the electron Compton wavelength. With a 720 degree rotation to complete a spin cycle, this circumference is consistant with wavelength. With gravitational collapse, angular momentum is conserved. The resulting black hole will have zero temperature as long as its spin is maximal. If its angular momentum is not retained (reduced to zero by merging with a positron antiparticle) it will immediately become hot, explode and lose all of its mass by Hawking radiation. DonJStevens 22:42, 10 March 2007 (UTC)

Balanced pattern
When lengths labeled (L1) and (L4) are compared to lengths previously labeled (L2) and (L3) an interesting ratio pattern appears.

L1 = 2pi (Planck length)(3/2) exp 1/2

L2 = 1/2 (Le)

L3 = (2pi)squared times (one light second)

L4 = 2pi (3Gm/c squared)

A balanced ratio pattern follows.

L1/L2 = L2/L3 = L4/L1 = 2(L1)/Le = Le/2(L3) = (L4/L2) exp 1/2 = (L4/L3) exp 1/3

When the implied G value is used, these dimensionless ratios are all equal. In the following equation, the G value will cancel so that the equation is correct without regard to a true G value.

L4/L2 = (L1/L2) squared

The above equation can be solved for (L1) to show that (L1) squared is (3pi hG/c cubed). This (L1) value is 2pi (Planck length) times (3/2) exponent 1/2. The gravitational time dilation ratio at the (L4) circumference is required to be equal to (L1/L2) and also equal to (L2/L3). This restricts the electron mass so that all electrons are identical. The equations below are derived from the balanced ratio pattern.

2(L4)/Le = [Le/2(L3)] squared

L4/L3 = (L2/L3) exp 3

(2pi) exp 5,(3Gm) = (L2) exp 3

The above equation defines the wavelength (L2) as a direct function of the gravitational constant and the electron mass.

(2pi) exp 5,(3G)(h/2c) = (L2) exp 4

2pi (3pi hG/c) exp 1/4 = L2

4pi (3pi hG/c) exp 1/4 = Le

There is no known reason why these equations should apply to the electron if the electron is not incredibly small and stabilized by its self-gravitational attraction. The balanced pattern results from relationships that are readily verifiable.---DonJStevens 19:57, 16 March 2007 (UTC)

The relationship, L1/L2 = L2/L3 can be altered so that the gravitational constant will cancel, as shown.

(L1) exp 1/2,divided by (L2) = (L2/L3)(1/L1) exp 1/2

With L2 equal to 2pi(3pi hG/c) exp 1/4 and (L1) exp 1/2 equal to (3pi hG/c cubed) exp 1/4, the G values cancel so that the ratio equation shown is correct without using a precise value for the constant G. However, the value 2(L2) or 4pi (3pi hG/c) exp 1/4 will be equal to the electron Compton wavelength only if the G value is (very close to) 6.6717456x10 exp-11. ---DonJStevens (talk) 17:40, 19 December 2007 (UTC)

This "Balanced pattern" shows that general relativity and quantum mechanics can merge without conflict.DonJStevens (talk) 15:13, 14 June 2009 (UTC)

Quantum - gravitational effect
At the extreme high energy photon wavelength (L1), a critical energy density is reached. This wavelength photon has energy equal to the mass energy of two black holes. Each of these black holes has a photon capture circumference [2pi (3Gm/c squared)] equal to the photon wavelength.

E = hc/L1 = 2E black hole = L1 (c exp 4)(1/3pi G)

hc/L1 = L1 (c exp 4)(1/3pi G)

L1 = (3pi hG/c cubed) exp 1/2

The (L1) wavelength photon is an effective model for all photons because photon energy is inversely proportional to wavelength. The (L1) wavelength provides a useful conversion factor to relate the Planck constant to the gravitational constant.

(L1) squared, (c cubed/3pi) = hG

(L1) squared, (c cubed/3pi h) = G

(L1) squared, (c cubed/3pi G) = h

When (L1) and G are known, h can be derived. The Planck length to electron Compton wavelength relationship (shown earlier) is known to be either precisely correct, as implied or extremely close to correct, as is clearly demonstrated.

(L2) squared = (L3)(L1)

Full confirmation of this relationship would allow the electron to be correctly defined as a "quantum - gravitational" mass particle as shown below. This is significant because it would raise our understanding of particles to a new level.

m = (h/4pi c)(c/3pi hG) exp 1/4

The derived electron mass formula, like the black hole entropy formula, contains the Planck constant as well as the gravitational constant, indicating that the electron mass value is the result of a quantum - gravitational effect. See page 715,in "The Road To Reality" by Penrose.

DonJStevens 15:37, 24 March 2007 (UTC)

Constants; one too many
In 1963, P.A.M. Dirac wrote an article titled "The Evolution Of The Physicist's Picture Of Nature". He predicted, the physics of the future, "--- cannot have the three quantities h bar, e and c all as fundamental quantities". Dirac wrote, "I think one is on safe ground if one makes the guess that --- e and c will be fundamental and h bar will be derived".

As noted under Matter-wave quantum, the Planck constant can be derived from the electron mass, light velocity and the gravitational constant.

h = 2mc(3Gm)exp 1/3, times(2pi)exp 5/3

h/2pi = 2mc[12(pi squared)Gm]exp 1/3  DonJStevens 15:27, 24 August 2007 (UTC)

Dirac said another problem to be solved is, "--- how to introduce the fundamental length (Planck length) to physics in some natural way ---". The natural way described here shows that the electron Compton wavelength is a function of the Planck length.

DonJStevens 15:30, 24 April 2007 (UTC)]]

Recent edits
Don -

A lot of stuff that is somewhere between speculative and wring have ended up in the this article recently. First of all singulatities usually exist behind an event horizon, and so are useless in describing the chataceristics of an electron. This also applies to the ring singularity of the Kerr metric.

I also have my doubts that gravitaition can solve the "stability problem" for the electron as gravitation is repulsive when one gets close enough that a charged enough particle. (GR loves to pull stunts like that.) Even so, that statement is quite permissible if you can provide an explicit reference in which Greene and MacGregor make this claim.

Overall, I am wondering if this article may not be better off by being rolled back a month or two. --EMS | Talk 16:58, 26 April 2007 (UTC)

P.S. I also wonder what you thing you are doing with the numerology given above. I once did check out a speculation like your Plank's constant one once and found it to diverge in the 4th decimal place. Without a sound theoretical basis for that supposed connection, nothing like that is going to work, and I see no such basis here. --EMS | Talk 16:58, 26 April 2007 (UTC)


 * Answer; The relationships I have described are consistant and easy to verify. I believe they can help to develop a better understanding of electrons, though you have said they are just numerology. I will respect your opinion and still disagree, knowing that whatever is correct will eventually prevail. A quote from Brian Greene, from his book The Elegant Universe (page 333) follows; "For many years, some of the most accomplished theoretical physicists speculated about the possibility of space-tearing processes and of a connection between black holes and elementary particles. Although such speculations might have sounded like science fiction at first, the discovery of string theory, with its ability to merge general relativity and quantum mechanics, has allowed us now to plant these possibilities firmly at the forefront of cutting-edge science". Much more info. is presented pages 320 through 344.


 * If you have acces to "The Enigmatic Electron" book by Malcolm MacGregor you can see his comment on page 72 regarding electrons: no combination of electric and magnetic forces has been proposed that can produce a stable state. Gravitational forces could solve the stability problem if the electron is extremely small and dense. This is from notes that I took when reading. I don't have this book in my library.
 * DonJStevens 19:02, 27 April 2007 (UTC)


 * Thank you much. Please plave those references into the article. --EMS | Talk 19:49, 27 April 2007 (UTC)


 * References have been added. I share your concern regarding the event horizon. The electron properties indicate (a) squared should equal (m) squared if it is an "extreme Kerr" black hole. This suggests that the charge (e) is just a reflected property of a collapsed (stationary) electromagnetic wave. The wave is stationary due to inertial frame dragging. If an electric charge can produce an electromagnetic wave, can an electromagnetic wave produce a charge? Clearly, the answer is yes but the wave must produce a pair of opposing charges and an energy threshold must be met before this can happen.    --DonJStevens 15:00, 29 April 2007 (UTC)
 * Note that for the Reissner-Nordstrom metric (solution of Einstein-Maxwell equations) the condition for the black hole to be extremal with zero temperature, is m = e rather than m squared = a squared plus e squared.---DonJStevens 17:46, 27 May 2007 (UTC)

I've been following the micro black hole speculation for perhaps 15 years without before discovering the black hole electron, so my guess is; it is not mainstream opinion. I suspect quantum physics is well supported by math, but seriously lacking in experimental and observational support. Much of quantum physics could diasappear in the coming century, unlike the physics of Sir Isaac Newton which may endure forever. Neil
 * Neil;The black hole electron concept relates to string theory and quantum gravity evaluations. This concept can become mainstream opinion only when further evaluations are completed to more precisely explain how general relativity and quantum mechanics merge. Note that electron properties imply that gravitational time dilation (and space contraction) become quantized when the relative time rate approaches zero seconds per second. The twin gravitational effects of time dilation and space contraction are then required to be quantized.--DonJStevens 16:40, 3 August--DonJStevens 14:22, 5 August 2007 (UTC) 2007 (UTC)

Matter-antimatter wormhole?
Wouldn't the electron-postitron pair imply a micro-wormhole between them if this idea is correct? --Ceriel Nosforit 07:37, 16 May 2007 (UTC)


 * I made pictures to show what I mean. The first one shows the electron black hole on top with a wormhole down to the positron black hole. They are connected on the same... membrane? - The second pic shows what happens when you take all the unnecessary dimension out and shrink the matter-antimatter pair to its smallest possible size. Side-view to the left and front-view to the right.
 * http://i8.tinypic.com/6ew2vsj.gif
 * http://i3.tinypic.com/54kdvyu.gif
 * I, for one, think it's elegant. :)
 * --Ceriel Nosforit 11:16, 16 May 2007 (UTC)
 * It might imply that, and it might be elegant, but wikipedia is concerned with WP:A and WP:OR, so until the concept can be attributable, we don't include it here. McKay 15:45, 16 May 2007 (UTC)
 * Ceriel;Many theorists would like to know the answer to your question. You may find words by Wheeler in his book "Geons, Black Holes and Quantum Foam"(page 239) are interesting, where he notes that with "curved" space, lines of electric field can "disappear" and still not be lost to the universe.DonJStevens 00:44, 19 May 2007 (UTC)
 * Cerial; You must see page 1200 in book "Gravitation" (Misner, Thorne, Wheeler), "Electric charge as lines of force trapped in topology of space". "Lines of force nowhere end. Maxwell's equations nowhere fail." You will appreciate the illustration. DonJStevens 15:24, 26 May 2007 (UTC)
 * Now that is one horribly expensive book... :( I'll keep checking back to the Amazon page to see if I can get a used copy cheaper. But thank you very much for the tip. BTW, I figure all fermions would work according to the same principle as the electron, and that bosons don't have holes in them but would rather be vibrations traveling through the same medium. Also, it seems the rather unintuitive properties of gyroscopes will lend me a bit more insight into how this stuff works. ...The musings continue. :)
 * Ceriel; added reply. For more insight into how this stuff works, look at my User page. More information and references are provided there that may not be appropriate for this article.--DonJStevens 13:51, 7 August 2007 (UTC)

Naked singularity
Stephen Hawking recently conceded that the laws of nature do permit a naked singularity to be formed during a gravitational implosion (collapse). This was the subject of a wager between Stephen Hawking and Kip Thorne. Hawking conceded when a naked singularity was produced in an implosion simulated on a computer.--DonJStevens 11:40, 16 October 2007 (UTC) This brings theorists one step closer to accepting the Burinskii concept that the electron spinning particle is a naked singular ring.--DonJStevens 01:15, 21 October 2007 (UTC) A naked singular ring electron (without an event horizon) is not a black hole but is a quantum gravitationally confined entity that has some properties in common with a black hole.--DonJStevens (talk) 13:11, 31 May 2008 (UTC)

Decay and conservation of charge
Forgive the "undergraduate question", but the argument that an electron black hole should immediately decay into a shower of photons ignores the question of conservation of charge. Could it be that the electron charge somehow "stabilizes" the particle?

So when a positron and an electron collide, the charge is neutralized. Now the resulting "larger mass black hole" CAN decay.

Into two photons instead of a shower of them? That bit about the mass equation? I'm willing to chalk these minor issues up to some future fusion of relativity and quantum theory. —Preceding unsigned comment added by 72.83.119.172 (talk) 01:36, 3 July 2008 (UTC)

Reply: In the toroidal topology electron model, the electron charge is the result of spin. When an electron and positron come together their opposite angular momentum values are added so that they cancel. Without angular momentum, there is no charge and no photon confinement. In this model spin stabilizes the particle.--DonJStevens (talk) 15:42, 4 July 2008 (UTC)

Mass as an energy of gravitationally confined photons
Thinking about mass and particles it occurred to me that mass could be completely eliminated from physics if particles could be treated as electromagnetic waves gravitationally confined in spacetime wrapped by the presence of EM energy.

Now after reading this article and discussion page it looks like model of electron discussed here is a realization of a similar (if not the same) idea but I am still not 100% sure.

Can you please tell me if this is the case? Are the results presented here compatible with a model in which electron is a photon propagating along a toroidal singularity?

It seems like a really nice idea, tying many loose ends. I certainly hope it will be researched more.Enemyunknown (talk) 23:50, 12 September 2008 (UTC)

Reply: The results presented are compatible with "a model in which electron is a photon propogating along a toroidal singularity", and also compatible with light velocity inertial frame dragging of the toroidal singularity. --DonJStevens (talk) 12:52, 13 September 2008 (UTC)

Added Reply: Later evaluations suggest that an electromagnetic geon, consisting of a single photon in a one wavelength loop is not stable. The electromagnetic geon appears to morph into a pair of gravitational wave geons. This pair of geons (particles) each has light velocity reference frame spin. Each particle has 1/2 of the electromagnetic geon energy and 1/2 of the electromagnetic geon angular momentum. --User:DonJStevens

Electron as quantum gravitational resonator
In the gravitationally collapsed electron model, the electron radius is equal to the (electron Compton wavelength /4pi) times (Gtf). The (Gtf) value is the gravitational time dilation factor that applies at the photon sphere radius (3Gm/c^2).

r1 = (Le/4pi) (Gtf) = (3/2)^1/2 (Planck length)

r2 = (Le/4pi) (Gtf)^2 = 3Gm/c^2

The r2 value is the result of gravitational blue shift and an equal amount of gravitational space contraction.

In this model, the resonance frequency of electron resonator is:

frequency = mc^2/h = E/h = c/Le

DonJStevens (talk) 18:31, 31 July 2009 (UTC)DonJStevens (talk) 12:29, 2 August 2009 (UTC)

As i understood, you used the following radiuses:
 * $$r_1 \approx \lambda_0(\frac{m_0}{m_P})^1 \ $$
 * $$r_2 \approx \lambda_0(\frac{m_0}{m_P})^2, \ $$

where $$m_0 - \ $$ rest mass of electron, $$\lambda_0 = \frac{h}{cm_0} - \ $$ electron Compton wavelength, $$m_P = \sqrt{\frac{c\hbar}{G}}- \ $$ Planck mass. What connections between electron resonator (electromagnetic or gravitational) model and these scales? 195.47.212.108 (talk) 06:44, 18 August 2009 (UTC)

I don't know the relationships between electron and Planck mass. So, I don't know the "derivation" of gravitational constant. I am suspicious to "numerology", "piramidology", etc. However, as a zero approach, some numerological steps could be done. But without strict physical approach any numerological attempts are useless. Sorry, but latest approach to electrogravity (by JERRY E. BAYLES) also is based on numerology and piramidology (nothing to say about trivial errors). 195.47.212.108 (talk) 07:19, 18 August 2009 (UTC)

Reply: The electron mass is equal to (Planck mass)(1/2)(2/3)^1/2 times the time dilation factor [(3/2)^1/2 (Planck time)(1/2pi seconds)]^1/2. The (Gtf) value is the time factor applicable at the electron photon orbit radius (3Gm/c^2).

(Gtf) = [(3/2)^1/2 (Planck time)(1/2pi seconds)]^1/2

(Gtf)^2 = (3/2)^1/2 (Planck time) (1/2pi seconds)

The electron mass value (h/4pi c)(c/3pi hG)^1/4 is precisely correct when G is equal to (Le/4pi)^3 (1/2pi)^2 (1/3m), where (Le) is the electron Compton wavelength and (m) is the electron mass. DonJStevens (talk) 15:16, 18 August 2009 (UTC)

Reply: Standard definition of the dielectric constant is:
 * $$\epsilon_E = \frac{e^2}{2hc\alpha_E} = \frac{1}{2c\alpha_E}\cdot \frac{1}{R_{HE}} \ $$

where $$R_{HE} = \frac{h}{e^2} \ $$ is the electromagnetic von Klitzing constant. Standard definition of the gravitational dielectric-like constant is:
 * $$\epsilon_G = \frac{m_{\alpha}^2}{2hc\alpha_G} = \frac{1}{2c\alpha_G}\cdot \frac{1}{R_{HG}} \ $$

where $$R_{HG} = \frac{h}{m_{\alpha}^2} \ $$ is the gravitational von Klitzing constant. Considering that $$\epsilon_G \ $$ is connectet with $$G \ $$ by:
 * $$G = \frac{1}{4\pi \epsilon_G} = \frac{c\alpha_G}{2\pi}\cdot R_{HG} \ $$

This is the only correct definition of $$G \ $$ ($$\alpha_G = \alpha_E \ $$), based on the Maxwell-like gravitational equations.

Sorry, I don't understand yours formulae... Please, use the standard Wiki formulae lenguage, to be clear... I try to consider some yours formulae, but it looks like pure numerology, since its dimensions are incorrect. For example, known JERRY E. BAYLES used the base velosity in the form:
 * $$v_{LM} = \sqrt{\alpha} \cdot 1m/s. \ $$

This is the pure numerology.
 * As you could see, all changes are gone... So, we have no ground to discuss. But I would be pleased, when you present the formulae in the clear form... 195.47.212.108 (talk) 10:33, 19 August 2009 (UTC)


 * Deleted text:

Electron as quantum gravitational resonator
Compton wavelength of electron is:
 * $$\lambda_0 = \frac{h}{m_0c}. \ $$

Electron radius in the quantum resonator approach is:
 * $$r_e = \frac{\lambda_0}{2\pi \sqrt{2}} = \lambda_0\cdot \frac{\rho_{G0}}{\rho_{Gc}}, \ $$

where
 * $$\rho_{G0} = \sqrt{\frac{\mu_G}{\epsilon_G}} = \frac{4\pi G}{c} = 2\alpha\cdot \frac{h}{m_{\alpha}^2} $$

is the gravitational vacuum characteristic impedance; $$\mu_G = \frac{4\pi G}{c^2}\ $$ is the gravitational vacuum permeability, $$\epsilon_G = \frac{1}{4\pi G} \ $$ is gravitational permittivity of vacuum and
 * $$\rho_{Gc} = \frac{v_cr_c}{m_{\alpha}} = \sqrt{2}\frac{G}{c} = \frac{\alpha}{\pi \sqrt{2}}\cdot \frac{h}{m_{\alpha}^2} \ $$

is the Planck mass black hole impedance, $$v_c = c/\sqrt{2} \ $$, $$m_P = \sqrt{\frac{G}{\hbar c}} \ $$, $$m_{\alpha} = \sqrt{\alpha}m_P \ $$. So, to the "black hole" mode closer the Planck mass (presenting in the real word "electric charge"), but not the inertial mass of electron ($$m_0 \ $$). The last is the fundamental constant of Nature and is independent of Planck mass. Electron resonator surface:
 * $$S_e = 4\pi r_e^2 = \frac{\lambda_0^2}{2\pi}. \ $$

Gravitational quantum capacitance of electron resonator:
 * $$C_{Ge} = \frac{\epsilon_G}{\lambda_0}\cdot S_e. \ $$

Gravitational quantum inductance of electron resonator:
 * $$L_{Ge} = \frac{\mu_G}{\lambda_0}\cdot S_e. \ $$

Gravitational characteristic impedance of electron resonator:
 * $$\rho_{Ge} = \sqrt{\frac{L_{Ge}}{C_{Ge}}} = \sqrt{\frac{\mu_G}{\epsilon_G}} = 2\alpha \frac{h}{m_{\alpha}^2}. \ $$

Resonance frequency of electron resonator:
 * $$\omega_{Ge} = \frac{1}{\sqrt{L_{Ge}C_{Ge}}} = \frac{\lambda_0c}{S_e} = \frac{m_0c^2}{\hbar}. \ $$

Rotation velocity of the spherical electron resonator is:
 * $$v_{Ge} = \omega_{Ge}\cdot r_e = \frac{c}{\sqrt{2}}. \ $$

So, the electron resonator approach yields the same scale of rotation velocity as the black hole does(?). However, electron Schwarzschild radius is:
 * $$r_{Se} = \frac{2Gm_0}{c^2}. \ $$

The relationships between resonator and Schwarzschild radiuses will be:
 * $$\frac{r_e}{r_{Se}} = \frac{1}{2\sqrt{2}}(\frac{m_P}{m_0})^2. \ $$

Considering that, the resonator electron radius is much greater then the Schwarzschild radius, therefore electron couldn't be presented as "gravitational black hole". Furthermore, considering the Planck length scale:
 * $$\lambda_P = \frac{h}{cm_P} = \frac{h}{c}\sqrt{\frac{G}{c\hbar}}, \ $$

we could derive the following relationships of the electron Schwarzschild radius and the Planck length:
 * $$\frac{\lambda_P}{r_{Se}} = \pi(\frac{m_P}{m_0})^1. $$

This is another factor that electron isn't the "gravitational black hole". Note that, the main electron length parameters are interconnected by the following relationship:
 * $$\lambda_P^2 = \pi \lambda_0r_{Se}. \ $$

Another words, the Planck length scale is intermediate between Compton wavelength of electron and its Schwarzschild radius. Considering that the Planck mass Schwarzschild radius is:
 * $$r_{SP} = \frac{2Gm_P}{c^2} = \frac{\lambda_P}{\pi}, \ $$

therefore the above relatinship could be rewritten as:
 * $$\lambda_P\cdot r_{SP} = \lambda_0\cdot r_{Se} = \frac{2hG}{c^3}, \ $$

which is fundamental, and could be used for another elementary particles.

Standard classical "black hole approach"
Let us consider classical cilcular rotation. The centrifugal and gravitation force relationship is:
 * $$F_{cen} = \frac{mv_c^2}{r} = F_N = G\frac{mM}{r^2}, \ $$

where $$F_N \ $$ is the gravitational force. From this condition the cilcular velocity can be derived as:
 * $$v_c = \sqrt{\frac{GM}{r}}. $$

Note that parabolic velocity is:
 * $$v_p = \sqrt{2} v_c = \sqrt{2\frac{GM}{r}}.$$

When the parabolic velocity takes the value of light velocity:
 * $$v_p = c, \ $$

then the s.c. Schwarzschild radius can be derived:
 * $$r_S = \frac{2GM}{c^2}. \ $$

Note that, only the probe mass $$m \ $$ is rotating, but object mass $$M \ $$ could be steel. Furthermore, we controlled the cilcular and parabolic velocities, but the interaction force could be any (gravitational, electromagnetic, etc.). So, when we say that quantum resonator forces restrict electron size about $$r_e \ $$ radius, with above relationships between circular and parabolic velocities, then this electron is like black hole.

Electrical radius
Let us consider rotation of the charged probe mass $$m_0 \ $$ in the electric field:
 * $$F_{cen} = \frac{m_0v_{cE}^2}{r} = F_C = \frac{1}{4\pi \epsilon_E}\frac{e^2}{r^2}, \ $$

where $$F_C \ $$ is the Coulomb force, and $$\epsilon_E \ $$ is the dielectric constant. From this condition the cilcular velocity can be derived as:
 * $$v_{cE} = c\sqrt{\frac{r_0}{r}}, $$

where $$r_0 = \frac{\alpha \lambda_0}{2\pi} \ $$ is the classical electron radius. When the parabolic velocity takes the velocity of light value
 * $$v_{pE} = \sqrt{2}v_{cE} = c\sqrt{2\frac{r_0}{r}} = c, \ $$

then the s.c. Schwarzschild radius could be derived:
 * $$r_{SE} = 2r_0. \ $$

Gravitational radius
By analogically to electric force, the gravitational classical radius of electron could be derived from relationship:
 * $$m_0c^2 = \frac{1}{4\pi \epsilon_G}\frac{m_0^2}{r^2}, \ $$

where $$\epsilon_G \ $$ is the gravitational electric-like dielectric constant. So, the gravitational classical electron radius is:
 * $$r_{0G} = \frac{\alpha_G\lambda_0}{2\pi}\cdot (\frac{m_0}{m_{\alpha}})^2 = r_{0E}\cdot (\frac{m_0}{m_{\alpha}})^2 \ $$

where $$\alpha_E \ $$ is electrical fine structure constant, and $$\alpha_G \ $$ is the gravitational fine structure constant. Furthermore, this constants are equal to each other:
 * $$\alpha_E = \alpha_G. \ $$

Note that, the Schwarzschild radius is two-times greater then the classical gravitational radius:
 * $$r_{Se} = \frac{2Gm_0}{c^2} = 2r_{0E}\cdot (\frac{m_0}{m_{\alpha}})^2 = 2r_{0G}. \ $$

Transition to the classical electric radius
The work needed to transite electron from $$r_e \ $$ radius to $$r_{0E} \ $$ radius is:
 * $$A_E = \int_{r_{0E}}^{r_e} F_C(r)\, dr = \frac{e^2}{4\pi \epsilon_E}\cdot \frac{r_{0E} - r_e}{r_{0E}r_e} = -m_0c^2(\frac{1}{\alpha \sqrt{2}} - 1). \ $$

Therefore, to make lesser radius of electron by the Coulomb force require about 137-times more energy then the rest energy of electron. It is evidently, that such process couldn't happen spontaneously, like some collaps for example.

Transition to the classical gravitational radius
The work needed to transite electron from $$r_e \ $$ radius to $$r_{0E} \ $$ radius is:
 * $$A_G = \int_{r_{0G}}^{r_e} F_N(r)\, dr = \frac{m_0^2}{4\pi \epsilon_G}\cdot \frac{r_{0G} - r_e}{r_{0G}r_e} = -m_0c^2. \ $$

So, we need only the rest enegy of electron additionally to transite mass $$m_0 \ $$ to the classical gravitational radius. This is a small energy and could be easily realized by experimentally, but...   There are no particles without electric charge (compencated or not). So, we need to transport elementary electric charge with elementary mass. Transport electric work will be in that case:
 * $$A_{EG} = \int_{r_{0G}}^{r_e} F_C(r)\, dr = \frac{e^2}{4\pi \epsilon_E}\cdot \frac{r_{0G} - r_e}{r_{0G}r_e} = -m_0c^2(\frac{m_{\alpha}}{m_0})^2 . \ $$

Therefore, we have the great problem with electric charge transport, but not with inertial mass. Yes, the gravitation radius of electron could be achived experimentally by applying the great amount of external energy, but there are no any spontaneous process, like collapse which shortened electron radius without external energy.

Special relativity
It is known, that acselerated electron has the mass dependence on velocity:
 * $$m(v) = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}. \ $$

So, we could use the following energy relationship:
 * $$-A_{EG} = m_0c^2(\frac{m_{\alpha}}{m_0})^2 = m(v)c^2, \ $$

from which the maximal electron velocity can be derived:
 * $$v_{max} = c \sqrt{1 - (\frac{m_0}{m_{\alpha}})^4} \approx c[1 - \frac{1}{2}(\frac{m_0}{m_{\alpha}})^4]. \ $$

Probably, that this velocity is maximal to any inertial mass in the our Universe. 195.47.212.108 (talk) 11:16, 19 August 2009 (UTC)

Deleted text
As I think, the text was deletet for the following reason: because there are no any gravitational black holes. Actually, to collapse electron to the gravitational radius need great energy:
 * $$\Delta W = W_0 (\frac{m_{\alpha}}{m_0})^2 \approx 2\cdot 10^{42} MeV \ $$

This value is equivalent to the following mass:
 * $$M_x = \frac{e\Delta W }{c^2} \approx 4\cdot 10^{12} kg. \ $$

Furthermore, if we transvers the whole Moon mass to collapse electrons, its number will be about $$10^{10}$$. This is the tupical concentradion of electrons in the dielectric materials per $$cm^{-3}$$. 195.47.212.108 (talk) 11:49, 19 August 2009 (UTC)


 * It was deleted because it's original research. Please read WP:OR. -- BenRG (talk) 12:32, 19 August 2009 (UTC)
 * This is not oririnal investigation. Actually, in the Ross paper (Ross McPherson. Stoney Scale and Large Number Coincidences. Apeiron, Vol. 14, No. 3, July 2007) we could see the TWO different orbital velocities, due to gravity (gravitational speed), and due to elecricity (electromagnetic speed). Equating these velocities to the maximal parabolic velocity yields the s.c. Schwarzschild radius.195.47.212.108 (talk) 06:48, 25 August 2009 (UTC)

Reply: Yes, we have moved too far into original research. We expect the research discussion will continue (not in Wikipedia) because we need to explain how the electron mass is quantized and stable.DonJStevens (talk) 15:17, 19 August 2009 (UTC)

Added reply:Research discussion continues. See, http://www.absoluteastronomy.com/discussionpost/Electron_as_a_ring_singularity_56595

DonJStevens (talk) 13:50, 18 March 2011 (UTC)

Superluminal velocity?
In the section "Problems": "Quantum mechanics permits superluminal speeds for an object with as small a mass as the electron over distance scales larger than the Schwarzschild radius of the electron".

I don't believe quantum mechanics allows superluminal speeds, unless by that is meant some wave notion such as wave velocity or group velocity (signal velocity is always lower than that of light). Who wrote that sentence should explain it better, say why it should consitute a problem, and provide references. Otherwise the section should be removed --131.130.45.41 (talk) 14:09, 30 August 2011 (UTC).

Reply: Alexander Burinskii has theorized that electron angular momentum (J = h bar/2) is so high that black hole horizons disappear. With this concept, the electron spinning ring is a naked singularity that is larger than its Schwarzschild radius. With the larger radius, superluminal speed is not required. The light orbit radius value, 3Gm/c^2 provides good numerical agreement with a number of known electron properties. DonJStevens (talk) 21:56, 26 September 2011 (UTC)

New changes
I'm trying to fix up this article a bit, to make it better express standard views on physics, and to provide references for all the claims made. I'm a mathematical physicist and an expert on general relativity and quantum field theory, so I think I can do this. John Baez (talk) 12:35, 6 September 2016 (UTC)

better explanation possible?
The text says:

...In the Reissner–Nordström metric, which describes electrically charged but non-rotating black holes, there is a quantity r_q, defined by ... Since this (vastly) exceeds the Schwarzschild radius, the Reissner–Nordström metric has a naked singularity.

It would be great if r_q could be motivated a bit, what is it?--Haraldkir (talk) 12:16, 24 February 2019 (UTC)

Black hole muon?
Im curious if these calculations generalize to the other charged leptons such as the muon? 87.63.114.242 (talk) 05:37, 21 September 2023 (UTC)