On the Zeroth Law Thermodynamics of Black Hole

The inherent contradictions of the zeroth law of thermodynamics in Bekenstein black hole thermodynamics has been analysed. The results in this paper showed that, on the basis of the essential connotation of zeroth law of thermodynamics the black hole(including the stationary black hole) can't be the equilibrium systems, and so the expression for the temperature in black hole thermodynamics is only formal expression. Even so, if the time-space warps of gravitalional field are taken into consideration, the horizon-temperature may be formally introduced with the transmission of thermal equilibrium in the horizon of black hole, but this temperature is not arbitrary value, it must be horizen-temperature controlled by kinetic parameter, the horizon acceleration κ_+. Therefore, the transmission of thermal equilibrium in black hole not only must be limited to the horizon area, but also the value of temperature of tbermal equilibrium system must be the horizon-temperature. However since the energy of gravitational field must be negative, the horizon temperature can't be positive, it must be negative.