Exact solutions of the Einstein-Maxwell equations in the Kerr-Schild formalism are discussed. We show that black hole horizon is unstable with respect to electromagnetic excitations. Contrary to smooth harmonic functions used in perturbative solutions, the exact solutions for electromagnetic excitations on the Kerr background have the form of singular twistor-beams which have very strong back reaction to metric and break the black-hole horizon, forming in it holes which allow radiation to escape interior of black-hole. As a result, under action of the external electromagnetic field the horizon may be covered by a set of fluctuating micro-holes, which corresponds to a semi-classical mechanism of Hawking radiation.