  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.

Quantum Physics