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Extremal black holes that are not extremal: maximal warm holes
A bstract We study a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with nonzero Hawking temperature. The implications for Hawking evaporation are discussed.
Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10322657
Journal Name:
Journal of High Energy Physics
Volume:
2022
Issue:
1
ISSN:
1029-8479
4. A bstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$\sim {M}_i^2$$ ∼ M i 2 at late times, where M i is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $${M}_i^{2/3}$$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$\sim {M}_i^2$$ ∼ M i 2more »