# Extremal black hole

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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.

The five-dimensional black hole can be derived as a solution of the low-energy effective
action for string compactification down to five dimensions:
S5 =Zd5x√−ge−2φ�R + 4(∇φ)2 − 13H2�

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 alsoEdit

## NotesEdit

**^**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.**^**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.**^**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.

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