Black hole electron

Short description: Hypothetical concept in physics

In physics, there is a speculative hypothesis that, if there were a black hole with the same mass, charge and angular momentum as an electron, it would share other properties of the electron. Most notably, Brandon Carter showed in 1968 that the magnetic moment of such an object would match that of an electron.[1] This is interesting because calculations ignoring special relativity and treating the electron as a small rotating sphere of charge give a magnetic moment roughly half the experimental value (see Gyromagnetic ratio).

However, Carter's calculations also show that a would-be black hole with these parameters would be "super-extremal". Thus, unlike a true black hole, this object would display a naked singularity, meaning a singularity in spacetime not hidden behind an event horizon. It would also give rise to closed timelike curves.

Standard quantum electrodynamics (QED), currently the most comprehensive theory of particles, treats the electron as a point particle. There is no evidence that the electron is a black hole (or naked singularity) or not. Furthermore, since the electron is quantum-mechanical in nature, any description purely in terms of general relativity is paradoxical until a better model based on understanding of quantum nature of blackholes and gravitational behaviour of quantum particles is developed by research. Hence, the idea of a black hole electron remains strictly hypothetical.

## Contents

* 1 Details
* 2 See also
* 3 References
* 4 Further reading
* 4.1 Popular literature

## Details

An article published in 1938 by Albert Einstein, Leopold Infeld, and Banesh Hoffmann showed that if elementary particles are treated as singularities in spacetime it is unnecessary to postulate geodesic motion as part of general relativity.[2] The electron may be treated as such a singularity.

If one ignores the electron's angular momentum and charge, as well as the effects of quantum mechanics, one can treat the electron as a black hole and attempt to compute its radius. The Schwarzschild radius rs of a mass m is the radius of the event horizon for a non-rotating uncharged black hole of that mass. It is given by rs=2Gmc2, where G is the Newtonian constant of gravitation, and c is the speed of light. For the electron,

m = 9.109×10−31 kg,

rs = 1.353×10−57 m.

Thus, if we ignore the electric charge and angular momentum of the electron and naively apply general relativity on this very small length scale without taking quantum theory into account, a black hole of the electron's mass would have this radius.

In reality, physicists expect quantum-gravity effects to become significant even at much larger length scales, comparable to the Planck length ℓP=Gℏc3=1.616×10−35m.

So, the above purely classical calculation cannot be trusted. Furthermore, even classically, electric charge and angular momentum affect the properties of a black hole. To take them into account, while still ignoring quantum effects, one should use the Kerr–Newman metric. If we do, we find that the angular momentum and charge of the electron are too large for a black hole of the electron's mass: a Kerr–Newman object with such a large angular momentum and charge would instead be "super-extremal", displaying a naked singularity, meaning a singularity not shielded by an event horizon.

To see that this is so, it suffices to consider the electron's charge and neglect its angular momentum. In the Reissner–Nordström metric, which describes electrically charged but non-rotating black holes, there is a quantity rq, defined by rq=q2G4πϵ0c4, where q is the electron's charge, and ε0 is the vacuum permittivity. For an electron with q = −e = −1.602×10−19 C, this gives a value

rq = 1.3807×10−36 m.

Since this (vastly) exceeds the Schwarzschild radius, the Reissner–Nordström metric has a naked singularity.

If we include the effects of the electron's rotation using the Kerr–Newman metric, there is still a naked singularity, which is now a ring singularity, and spacetime also has closed timelike curves. The size of this ring singularity is on the order of ra=Jmc, where as before m is the electron's mass, and c is the speed of light, but J = ℏ/2 is the spin angular momentum of the electron. This gives

ra = 1.9295×10−13 m,

which is much larger than the length scale rq associated with the electron's charge. As noted by Carter,[3] this length ra is on the order of the electron's Compton wavelength. Unlike the Compton wavelength, it is not quantum-mechanical in nature.

More recently, Alexander Burinskii has pursued the idea of treating the electron as a Kerr–Newman naked singularity.[4]

## See also

* Quantum gravity
* Abraham–Lorentz force
* Black hole thermodynamics
* Entropic force
* Hawking radiation
* List of quantum gravity researchers
* Entropic elasticity of an ideal chain
* Gravitation
* Induced gravity
* Geon
* Micro black hole
* Geometrodynamics

## References

1. ↑ Carter, B. (25 October 1968). "Global structure of the Kerr family of gravitational fields". Physical Review 174 (5): 1559–1571. doi:10.1103/physrev.174.1559. Bibcode: 1968PhRv..174.1559C.
2. ↑ Einstein, A.; Infeld, L.; Hoffmann, B. (January 1938). "The gravitational equations and the problem of motion". Annals of Mathematics. Second Series 39 (1): 65–100. doi:10.2307/1968714. Bibcode: 1938AnMat..39...65E.
3. ↑ Carter, B. (25 October 1968). "Global structure of the Kerr family of gravitational fields". Physical Review 174 (5): 1559–1571. doi:10.1103/physrev.174.1559. Bibcode: 1968PhRv..174.1559C.
4. ↑ Burinskii, Alexander (April 2008). "The Dirac-Kerr-Newman electron". Gravitation and Cosmology 14 (2): 109–122. doi:10.1134/S0202289308020011. Bibcode: 2008GrCo...14..109B.

## Further reading

* Duff, Michael (1994). Kaluza–Klein theory in perspective. Bibcode: 1995okml.book...22D.
* Hawking, Stephen (1971). "Gravitationally collapsed objects of very low mass". Monthly Notices of the Royal Astronomical Society 152: 75. doi:10.1093/mnras/152.1.75. Bibcode: 1971MNRAS.152...75H.
* Penrose, Roger (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. London: Jonathan Cape.
* Salam, Abdus. "Impact of quantum gravity theory on particle physics". in Isham, C. J.; Penrose, Roger; Sciama, Dennis William. Quantum Gravity: an Oxford Symposium. Oxford University Press.
* 't Hooft, Gerard (1990). "The black hole interpretation of string theory". Nuclear Physics B 335 (1): 138–154. doi:10.1016/0550-3213(90)90174-C. Bibcode: 1990NuPhB.335..138T.

### Popular literature

* Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (1999), (See chapter 13)
* John A. Wheeler, Geons, Black Holes & Quantum Foam (1998), (See chapter 10)

* v
* t
* e

Black holes

Types|

* Schwarzschild
* Rotating
* Charged
* Virtual
* Kugelblitz
* Primordial
* Planck particle

Size|

* Micro
* Extremal
* Electron
* Stellar
* Microquasar
* Intermediate-mass
* Supermassive
* Active galactic nucleus
* Quasar
* Blazar

Formation|

* Stellar evolution
* Gravitational collapse
* Neutron star
* Related links
* Tolman–Oppenheimer–Volkoff limit
* White dwarf
* Related links
* Supernova
* Related links
* Hypernova
* Gamma-ray burst
* Binary black hole

Properties|

* Gravitational singularity
* Ring singularity
* Theorems
* Event horizon
* Photon sphere
* Innermost stable circular orbit
* Ergosphere
* Penrose process
* Blandford–Znajek process
* Accretion disk
* Hawking radiation
* Gravitational lens
* Bondi accretion
* M–sigma relation
* Quasi-periodic oscillation
* Thermodynamics
* Immirzi parameter
* Schwarzschild radius
* Spaghettification

Issues|

* Black hole complementarity
* Information paradox
* Cosmic censorship
* ER=EPR
* Final parsec problem
* Firewall (physics)
* Holographic principle
* No-hair theorem

Metrics|

* Schwarzschild (Derivation)
* Kerr
* Reissner–Nordström
* Kerr–Newman
* Hayward

Alternatives|

* Nonsingular black hole models
* Black star
* Dark star
* Dark-energy star
* Gravastar
* Magnetospheric eternally collapsing object
* Planck star
* Q star
* Fuzzball

Analogs|

* Optical black hole
* Sonic black hole

Lists|

* Black holes
* Most massive
* Nearest
* Quasars
* Microquasars

Related|

* Black Hole Initiative
* Black hole starship
* Compact star
* Exotic star
* Quark star
* Preon star
* Gamma-ray burst progenitors
* Gravity well
* Hypercompact stellar system
* Membrane paradigm
* Naked singularity
* Quasi-star
* Rossi X-ray Timing Explorer
* Timeline of black hole physics
* White hole
* Wormhole

* Category
* Commons

0.00

(0 votes)

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Astronomy:Black_hole_electron&oldid=4201131"
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template