Compensate Effect Under Time-Scale Transformation in Vaidya-Bonner Space-Time

The Hawking effect in the Vaidya-Bonner space-time can be considered as a compensate effect of the scale transformation of coordinate time. The gauge potential is the contraction of the affine connection. It is found that the rate of change of temperature can be obtained as the pure gauge potential of the compensate field, in addition to the Hawking temperature which was known from the stationary black holes.