Microscopic entropy of AdS3 black holes revisited

We revisit the microscopic description of AdS$_3$ black holes in light recent progress on their higher dimensional analogues. The grand canonical partition function that follows from AdS$_3$/CFT$_2$ correspondence describes BPS and nearBPS hole thermodynamics. formulate an entropy extremization principle accounts for both a constraint its charges, close analogy with asymptotically AdS dimensions. are led to interpret supersymmetric as ensembles microstates satisfying charge is not respected by individual states. This interpretation provides understanding hitherto mysterious constraints satisfied all AdS. also develop thermodynamics nAttractor mechanism regime.