Quantum field theory in two-dimensional schwarzschild-de sitter space-time 1. empty space, Prog

A quantized conformal scalar field is studied in an empty two-dimensional Schwarzschild·de Sitter spacetime, which has two kinds of horizons. It is shown that there is a quantum state such that the renormalized expectation value of the stress tensor operator in the state is regular everywhere in the spacetime. We present an example of such a state in which the stress tensor not only respects the de Sitter symmetry asymptotically in the past and future but is also static in a substantial part of the spacetime