= Particle creation by a nonstationary spacetime
{title2=$\langle N_i^{\rm out}\rangle_{\rm in}=\sum_j|\beta_{ij}|^2$}
= Gravitational particle creation
{synonym}
Positive-frequency modes in stationary asymptotic past and future regions can differ by a <Bogoliubov transformation> mixing positive and negative frequency solutions. The conserved <Klein-Gordon inner product> gives its canonical normalization. The out annihilation operator then contains in creation operators, yielding the displayed number expectation in the initial vacuum. A nonzero mixing coefficient changes the particle content relative to final observers without violating deterministic field evolution.
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