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Degrees of freedom that carry black hole entropy and hair can be described inthe language of Goldstone phenomenon. They represent the pseudo-Goldstonebosons of certain supertranslations, called A-transformations, that arespontaneously broken by the black hole metric. This breaking gives rise to atower of Goldstone bosons created by the spontaneously-broken generators thatcan be labeled by spherical harmonics. Classically, the number of charges isinfinite, they have vanishing VEVs and the corresponding Goldstone modes aregapless. The resulting hair and entropy are infinite, but unresolvable. Inquantum theory the two things happen. The number of legitimate Goldstone modesrestricted by requirement of weak-coupling, becomes finite and scales as blackhole area in Planck units. The Goldstones generate a tiny gap, controlled bytheir gravitational coupling. The gap turns out to be equal to the inverse ofblack hole half-life, $t_{BH}$. Correspondingly, in quantum theory the chargesare neither conserved nor vanish, but non-conservation time is set by $t_{BH}$.This picture nicely matches with the idea of a black hole as of critical systemcomposed of many soft gravitons. The A-Goldstones of geometric picturerepresent the near-gapless Bogoliubov-Goldstone modes of critical soft-gravitonsystem.

Goldstone origin of black hole hair from supertranslations and criticality