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The quantum entropy of the Kerr black hole arising from gravitationalperturbation is investigated by using Null tetrad and \'t Hooft\'s brick-wallmodel. It is shown that effect of the graviton\'s spins on the subleadingcorrection is dependent of the square of the spins and the angular momentum perunit mass of the black hole, and contribution of the logarithmic term to theentropy will be positive, zero, and negative for different value of $a/r_+$.Comment: 8 pages, 1 figure, Latex. to appear in Phys. Rev.

Quantum entropy of the Kerr black hole arising from gravitational perturbation