More on the Entropy Product and Dual CFTs

In this paper, we check the universality of the entropy product for some black hole and black ring solutions. Applying the asymptotic symmetry group (ASG) analysis, we also find the central charges of the dual CFTs for these solutions. It has been observed \cite{Chen:2013rb} that if the entropy product for a solution is universal, it is possible to read the central charges of the dual CFTs from the entropy product as $c_i \sim \frac{\partial}{\partial N_i}(S_+S_-)$, where $N_i$ is a conserved charge of the solution like angular momentum or electric charge. In this work, we consider some other families of solutions and we check that the same behavior is valid for them. Moreover, in the case of solutions containing the conical singularity, we find the central charges using the ASG analysis. We show that the central charges receive a contribution from the conical characteristic $κ$ of the solution, however it is still possible to read the central charges from the entropy product.

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