A note on the Cardy-Verlinde formula

We study static, spherically symmetric, and asymptotically AdS black hole spacetimes with matter distribution satisfying Ttt=Trr. The first law of black hole thermodynamics is checked. We show that the Cardy-Verlinde formula, which is supposed to be an entropy formula of CFTs in any dimensions, is just a rewritten form of Einstein equations on the black hole horizon. Further, the entropy of dual CFT to the black hole solution is found to indeed satisfy the Cardy-Verlinde formula and the energy of matter outside the black hole should be subtracted from the total energy of the dual CFT in the Cardy-Verlinde formula. The implications of our results are discussed.