Quantization of systems in incomplete spaces and the problem of particle production by a gravitational field

The space of a uniformly accelerated observer is regarded as a model of the neighborhood of a black hole. It is shown that a procedure of quantization in a uniformly accelerated system can be constructed in such a way that the Hamiltonian of the field remains self-adjoint, as it must under coordinate transformations. As a consequence of this, there is no thermal excitation background of the field in the uniformly accelerated system.