Abstract
The Unruh effect is considered for the case of a massless scalar field in an (1+1)D space-time. It is shown that under some natural assumptions like finitness of the integration volume or finitness of the interaction propagation speed the effect should be anisotropic.
Highlights
IntroductionMore than forty years ago Hawking [1, 2] and Unruh [3] showed that an observer set into a gravitational field of local strength a (or uniformly accelerated in a Minkowski space-time with acceleration a) will register thermal emission with the temperature THU (the HawkingUnruh temperature) defined as THU
More than forty years ago Hawking [1, 2] and Unruh [3] showed that an observer set into a gravitational field of local strength a will register thermal emission with the temperature THU defined as where is the Planck constant, c is the speed of light, kB is the Boltzmann constant
We consider the most simple case of a field – a massless scalar field in an (1+1)D space-time1. Within such a simple setup, certain corrections to the standard treatment of the Unruh effect are discussed below to reveal its possible anisotropy. In this investigation we focus on the properties of the distribution function of the Unruh radiation without consideration of any specific detector or its interaction with the quantum field
Summary
More than forty years ago Hawking [1, 2] and Unruh [3] showed that an observer set into a gravitational field of local strength a (or uniformly accelerated in a Minkowski space-time with acceleration a) will register thermal emission with the temperature THU (the HawkingUnruh temperature) defined as THU. Expression (11) shows that any rule of the relative behaviour of ρ1 and τ, which provides increasing ρ1 slower than exp (aτ/c), will lead to the zero value of Bogoliubov coefficient Note, that such behaviour of the integration limit corresponds to the law of motion of massless particles (quanta, e.g., photons) emitted at the observer position in the forward direction at τ = 0+ (i.e., just after the beginning of the accelerated motion). For such wavelengths the appropriate limit of integration can be choosen as several units of ρ1 in the Rindler space (and several units of x1 in the Minkowski space). At least this value remains well within the observable part of the Universe
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