It has been proved in this paper that in general the horizons in 4-dimensional static Riemann spacetime will produce Hawking radiations and the radiative temperature is proportional to the surface gravity k of the horizon.This work is extended to the state that there exist electromagnetic fields. We point out that the static electric potential which effects Hawking radiative spectrum may originate from the electrie charge inside the hos,izoii as well as outside the hosizon.The Rindler radiations in uniform accelerated frames and the Hawking radiations from Schwarzsehild B. H., Keissner-Nordstrom B. H. as wall as Schwarzschild-de Sitter universe horizons are the special cases of our present general theory.It is pointed out that the equivalence principle Is still effective and Rindlerradiations do originate from the horizons of the Rindler frames of reference. Hawkingradiation only has relation with dynamic effect K near the horizon, but has no relation with curvature of the spaeetime.