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We discuss the problem of the quantization and dynamic evolution of a scalarfree field in the interior of a Schwarzschild black hole. A unitary approach tothe dynamics of the quantized field is proposed: a time-dependent Hamiltoniangoverning the Heisenberg equations is derived. It is found that the system isrepresented by a set of harmonic oscillators coupled via terms corresponding tothe creation and annihilation of pairs of particles and that the symmetryproperties of the spacetime, homogeneity and isotropy are obeyed by thecoupling terms in the Hamiltonian. It is shown that Heisenberg equations forannihilation and creation operators are transformed into ordinary differentialequations for appropriate Bogolyubov coefficients. Such a formulation leads toa general question concerning the possibility of gravitationally driveninstability, that is however excluded in this case.

Quantum phenomena inside a black hole: quantization of the scalar field iniside horizon in Schwarzschild spacetime