Summary: A new general way for researching the Hawking effect in the spherically symmetric or the plane-symmetric nonstatic space-times is proposed. The theoretical foundation of this way is laid. The Klein-Gordon equation must be reduced to the standard form of wave equation near an event horizon when a generalized tortoise coordinate is adopted. Then, both the Hawking radiation temperature and the equation determining the location of the event horizon are obtained automatically. When the radiation is weak, the first approximation of our result is the same as the approximate result obtained with the radiation back-reaction method.