Black Hole Thermodynamics And η-ξ Space-time

As two important projects in black hole thermodynamics, horizon and its surface gravity of black hole are directly related with the entropy of black hole and the temperature of radiation. Zhao Z has proved that the horizon is the basic causation of thermal effect. Formulacan be used to calculate the locations of horizon and the surfacegravities in black hole space-time and Rindler space-time respectively, but in a toy model of quantum field theory in curved space-time-η-ζ space-time, they are invalid. Thus the surface gravity of η-ζ space-time, i.e. the temperature of Hawking-Unruh effect is not touched before.The black hole thermodynamics and η-ζ space-time are briefly reviewed in chapters one and two. In the third chapter, the horizon location of η-ζ, space-time is determined in light of the geometrical explanation of horizon given by N.D. Birrell.Then the connection between the two definitions of surface gravity on the horizon, whichare the metric definition and the method derived from space-timeconformance , is discussed. The detailed calculation and the physical sense arepresented. It can be seen that the space-time conformal method is more universal, andis the further expression of in black hole space-times and Rindlerspace-time. On the basis of the above conclusion, κ of η-ζ space-time is obtained for the first time, the result is: it is equal to the exponent factor α in the transformation between η-ζ space-time and Minkowski space-time. This ending confirms that η-ζ space-time can be seen as the background space-time of finite-temperature field theory. At last, the reasons why fails in η-ζ space-time are pointed out.