In theoretical physics, an extremal black hole is a black hole with the minimal possible mass that can be compatible with a given charge and angular momentum.[1] In other words, this is the smallest possible black hole that can exist while rotating at a given fixed constant speed.

The concept of an extremal black hole is theoretical and none have thus far been observed in nature. However, many theories are based on their existence.

In supersymmetric theories, extremal black holes are often supersymmetric: they are invariant under several supercharges. This is a consequence of the BPS bound. Such black holes are stable and emit no Hawking radiation. Their black hole entropy[2] can be calculated in string theory.

It has been suggested by Sean Carroll that the entropy of an extremal black hole is equal to zero. Carroll explains the lack of entropy by creating a separate dimension for the black hole to exist within.[3]

The hypothetical black hole electron is super-extremal (having more charge and angular momentum than a black hole of its mass "should").

See also

Black hole information paradox

Black hole thermodynamics

Quantum gravity

Trans-Planckian problem

Notes

Kallosh, Renata; Linde, Andrei; Ortín, Tomás; Peet, Amanda; Van Proeyen, Antoine (1 December 1992). "Supersymmetry as a cosmic censor". Physical Review D. 46 (12): 5278–5302. arXiv:hep-th/9205027. Bibcode:1992PhRvD..46.5278K. doi:10.1103/PhysRevD.46.5278. PMID 10014916. S2CID 15736500.

Bekenstein, Jacob D. (1973). "Black Holes and Entropy". Physical Review D. 7 (8): 2333–2346. Bibcode:1973PhRvD...7.2333B. doi:10.1103/PhysRevD.7.2333.

Carroll, Sean M.; Johnson, Matthew C.; Randall, Lisa (2009). "Extremal limits and black hole entropy". Journal of High Energy Physics. 2009 (11): 109. arXiv:0901.0931. Bibcode:2009JHEP...11..109C. doi:10.1088/1126-6708/2009/11/109. S2CID 73604121.

External links

Extremal RN Black Hole

N =2 extremal black holes pdf

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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

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