Unruh radiation is the thermal flux measured by an accelerated observer moving through Minkowski spacetime. We study Unruh radiation as tunneling through a barrier. We use a WKB-like method to obtain the tunneling rate and the temperature of the Unruh radiation. The gravitational WKB method helps to highlight the subtle points that the tunneling rate should be written as the closed path integral of the canonical momentum, and for the case of the gravitational WKB problem, there is a timelike contribution to the tunneling rate arising from an imaginary change of the time coordinate upon crossing the horizon. This temporal contribution to the tunneling rate has no analog in the usual quantum mechanical WKB calculation. The derivation brings together many topics, including classical mechanics, relativity, relativistic field theory, quantum mechanics, statistical mechanics, and mathematical physics.
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