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چکیده
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In this paper we obtain the entropy formula of black hole solutions of minimal massive gravity (MMG) by the Tachikawa method [1]. Then we apply this formula for the Bañados-Teitelboim-Zanelli black hole solution.We find that the usual Bekenstein-Hawking entropy is modified. The modification comes from the Chern-Simons term and the new term in MMG. The contribution of the Chern-Simons term, which is proportional with the inner radius of the horizon, is not new, but the last term which is due to the new term of MMG, as usual is proportional to the outer radius of the horizon and is the new result. Then we show that the total entropy is consistent with the first law of thermodynamics. After that, we show that the total entropy can be reproduced exactly by the Cardy formula for the entropy of the dual boundary Conformal Field Theory. Finally, we show that the requirement of positive entropy imposes some restrictions on the space of the parameters of the MMG, but these restrictions are completely in agreement with the constraints on the coupling constants that come from the solution of the bulk vs boundary clash.
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