Equivalence Principle and Field Quantization in Curved Spacetime

TL;DR

This paper explores how the equivalence principle constrains field quantization in curved spacetime, linking local frames to phenomena like Hawking and Unruh radiation through a self-interacting spin-2 field analogy.

Contribution

It introduces a framework for quantizing fields locally in curved spacetime using freely falling frames, connecting gravity to quantum field effects near black holes.

Findings

Vacuum acts as a thermal bath with Unruh temperature at fixed distances from black holes.

Near the horizon, the vacuum temperature matches Hawking radiation.

Local quantization aligns with the equivalence principle and reproduces known thermal effects.

Abstract

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.