On quantum radiation in curved spacetime

In the context of quantum field theories in curved spacetime, we compute the effective action of the transition amplitude from vacuum to vacuum in the presence of an external gravitational field. The imaginary part of the resulted effective action determines the probability of vacuum decay via a quantum tunneling process, giving the rate and spectrum of particle creations. We show that (i) the gravitational field polarizes the vacuum and discretizes its spectrum; (ii) vacuum gains gravitational energy by such a polarization. On the basis of gravitational vacuum polarization, we discuss the quantum origin of vacuum decay in curved spacetime as pair-creations of particles and anti-particles. The thermal spectrum of particle creations is attributed to (i) the CPT invariance of pair-creations (annihilations) from (into) vacuum and (ii) vacuum acts as a reserve with the temperature determined by gravitational energy-gain.