Quantization of Horizon Area from Accelerating and Rotating Black Hole

Based on the ideas of adiabatic invariant quantity, and as a further study, adopting near horizon approximation, we attempt to quantize the horizon area of an accelerating and rotating black hole in two different coordinate frames. The area spectrum is obtained by imposing Bohr-Sommerfeld quantization rule and the laws of black hole thermodynamics to the modified adiabatic covariant action of the rotating black hole. The results show that the area spectrum of the black hole is , which confirms the initial proposal of Bekenstein.