High temperature AdS black holes are low temperature quantum phonon gases

We report a precise match between the high temperature $(D+2)$-dimensional Tangherlini-AdS black hole and the low temperature quantum phonon gas in $D$-dimensional nonmetallic crystals residing in $(D+1)$-dimensional flat spacetime. The match is realized by use of the recently proposed restricted phase space formalism for black hole thermodynamics, and the result can be viewed as a novel contribution to the AdS/CMT correspondence on a quantitative level.