: Strong gravitational fields near a black hole's event horizon polarize the vacuum, causing the black hole to emit thermal radiation and gradually lose mass.

This framework predicts several landmark effects that bridge the gap between thermodynamics, gravity, and quantum mechanics:

In flat (Minkowski) spacetime, Poincaré invariance provides a unique vacuum state and a global definition of "particles". In curved spacetime, these "crutches" disappear:

bj=∑i(αjiai+βji*ai†)b sub j equals sum over i of open paren alpha sub j i end-sub a sub i plus beta sub j i end-sub raised to the * power a sub i raised to the † power close paren If the "mixing coefficient" βjibeta sub j i end-sub is non-zero, the vacuum of the first observer (

: In the early, rapidly expanding universe, time-varying gravitational fields can "excite" the vacuum, creating elementary particles that seed the large-scale structure of the universe. Robert Wald - Quantum Field Theory in Curved Spacetime

. This approach serves as a robust approximation for environments where gravity is strong but quantum gravitational effects—such as fluctuations of the metric itself—are not yet dominant. 1. The Fundamental Shift: From Particles to Fields