Quest for particles production in the plane gravitational wave spacetime

Massless vector and scalar Green’s functions are obtained in closed form for a plane gravitational wave spacetime using three independent methods: direct solution of the Green-function equation and construction via the DeWitt and Hadamard recursive schemes. The results coincide exactly with the DeWitt–Schwinger expansion, indicating no massless particles production in this background. Contrasting interpretations, based on Bogolyubov coefficient calculations predicting massless particle creation, are also addressed.