Thermodynamics in rotating anti-de Sitter black holes with massive scalar field in three dimensions *

Abstract

We investigated the tendency in the variations of CFT2 when a rotating AdS(3) black hole changes because of the fluxes transferred by the scattering of a massive scalar field according to the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. The conserved quantities of the black hole are definitely constrained by the extremal condition. Moreover, the laws of thermodynamics provide a direction for the changes in the conserved quantities. Therefore, the black hole cannot be extremal under the scattering; this is naturally preferred. According to the relationship between the rotating AdS(3) black hole and dual CFT2, we find that such changes in the black hole constrain thevariations in the eigenstates of dual CFT2. Furthermore, the tendency in the variations is closely related to the laws of thermodynamics.