Microscopic Entropy of AdS$_3$ Black Holes Revisited

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