The equation of Unruh effect
The Unruh temperature, derived by William Unruh in 1976, is the effective temperature experienced by a uniformly accelerating detector in a vacuum field. It is given by
where 
is the local acceleration, 
is the Boltzmann constant, 
is the reduced Planck constant, and 
is the speed of light. Thus, for example, a proper acceleration of 2.5 × 1020 m s−2 corresponds approximately to a temperature of 1 K.
is the local acceleration, is the Boltzmann constant, is the reduced Planck constant, and is the speed of light. Thus, for example, a proper acceleration of 2.5 × 1020 m s−2 corresponds approximately to a temperature of 1 K.
The Unruh temperature has the same form as the Hawking temperature 
of a black hole, which was derived (by Stephen Hawking) independently around the same time. It is, therefore, sometimes called the Hawking–Unruh temperature.
of a black hole, which was derived (by Stephen Hawking) independently around the same time. It is, therefore, sometimes called the Hawking–Unruh temperature.
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