Extremal black hole
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In theoretical physics, an extremal black hole is a black hole with the minimum possible mass that is compatible with its charge and angular momentum.[1]
The concept of an extremal black hole is theoretical and none have thusfar 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 Hawking radiation of extremal black holes is considered non-thermal (non-Planck distributed), with no associated temperature.[4]
The hypothetical black hole electron is super-extremal (having more charge and angular momentum than a black hole of its mass "should").
The third law of black hole thermodynamics should disallow such an extremal black hole and in 1986 a proof was published[5] by Werner Israel nevertheless recent work in a pair of preprints claims it contains a error and therefore extremal black hole are indeed possible.[6][7][8] The third law of thermodynamics for black holes has always been controversial.
See also
[edit]- Black hole information paradox
- Black hole thermodynamics
- Near-extremal black hole
- Quantum gravity
- Trans-Planckian problem
- Positive energy theorem
Notes
[edit]- ^ 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". Phys. Rev. D. 7 (8): 2333–2346. Bibcode:1973PhRvD...7.2333B. doi:10.1103/PhysRevD.7.2333. S2CID 122636624.
- ^ 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.
- ^ Good, Michael (2020). "Extremal Hawking Radiation". Physical Review D. 101 (104050): 104050. arXiv:2003.07016. Bibcode:2020PhRvD.101j4050G. doi:10.1103/PhysRevD.101.104050. S2CID 212725670.
- ^ Israel, W. (1986-07-28). "Third Law of Black-Hole Dynamics: A Formulation and Proof". Physical Review Letters. 57 (4): 397–399. doi:10.1103/PhysRevLett.57.397. ISSN 0031-9007.
- ^ Kehle, Christoph; Unger, Ryan (2023-04-17), Event horizon gluing and black hole formation in vacuum: the very slowly rotating case, doi:10.48550/arXiv.2304.08455, retrieved 2024-08-27
- ^ Kehle, Christoph; Unger, Ryan (2024-02-15), Extremal black hole formation as a critical phenomenon, doi:10.48550/arXiv.2402.10190, retrieved 2024-08-27
- ^ "Mathematicians Prove Hawking Wrong About 'Extremal' Black Holes". Quanta Magazine. 2024-08-21. Retrieved 2024-08-27.
External links
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