Density matrix and generating functional for quantum processes in black holes

An expression for density matrix for the processes of production, absorption and scattering of particles by a rotating black hole is obtained. Using the density matrix the generating functional is calculated. The functional permits via differentiation to obtain expressions for probabilities of different quantum processes in black holes, spectra and correlation functions for the number of particles in arbitrary multiparticle initial states. Application of the ratios obtained in the following particular cases: particle production in vacuum, particle production from m-partial state and scattering of coherent wave on a black hole, is considered