  In this work I study the polarization of the Cosmic Microwave Background
(CMB) induced by a cosmological background of gravitational waves (here GWs)
and I discuss the enhancement effect of a possible late and fast reionization
of the Universe, caused by the Hawking evaporation of primordial black holes
and happening at a redshift $z\sim 20\div 30$. Then, I solve the radiative
Boltzmann transfer equation in the form of a second-kind Volterra integral
equation, by using the analytical method of the iterated kernels: this
particular method can be successfully applied when we have an exponential
kernel, as in the case when the Universe is reionized by the intense particle
emission coming from evaporating primordial black holes.
