Equivalence Principle and Field Quantization in Curved Spacetime

To comply with the equivalence principle, fields in curved spacetime can be quantized only in the neighborhood of each point, where one can construct a freely falling M i n k o w s k i frame with z e r o curvature. In each such frame, the geometric forces of gravity can be replaced by a selfinteracting spin-2 field, as proposed by Feynman in 1962. At a n y fixed distance $R$ from a black hole, the vacuum in each freely falling volume element acts like a thermal bath of all particles with Unruh temperature T_U=\hbar GM/2\pi c R^2. At the horizon R=2GM/c^2, the falling vacua show the Hawking temperature T_H=\hbar c^3/8\pi GMk_B.