Equivalence Principle and Field Quantization in Curved Spacetime

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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 Tᵤ=ℏ GM/2πc R². At the horizon R=2GM/c², the falling vacua show the Hawking temperature Tₕ=ℏ c³/8πGMkB.