Kerr/CFT correspondence on Kerr-Newman-NUT-Quintessence black hole

Abstract

Rotating black hole solution surrounded by quintessential matter is recently discussed because it might be the promising solution to study the effect of dark energy in small scale of the universe. This quintessential solution is originally derived from the condition of additivity and linearity for the energy-momentum tensor. We carry out the thermodynamic properties of this solution using the Kerr/CFT correspondence for several specific quintessential equation of state parameters. A problem arises when we compute the central charge because the canonical conserved charge is needed to be calculated from the Lagrangian. However, the exact Lagrangian of the quintessence is not defined yet in the original derivation. Yet we solve this problem by the assumption that there is only a contribution from gravitational field to the central charge. Then we could find the entropy of this black hole after calculating the temperature and using Cardy entropy formula. Another problem comes out when the spin goes to zero to find the Reissner-Nordstr\"om-NUT-Quintessence solution. To solve it, we extend to the 5-dimensional solution. In the end, we obtain the entropy for this 5-dimensional solution. So the quintessential black hole solution is dual with the CFT.