A WKB-like approach to Unruh Radiation

Abstract

Unruh radiation is the thermal flux seen by an accelerated observer moving through Minkowski spacetime. In this article 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. This derivation brings together many topics into a single problem - classical mechanics, relativity, relativistic field theory, quantum mechanics, thermodynamics and mathematical physics. Moreover, this gravitational WKB method helps to highlight the following subtle points: (i) the tunneling rate strictly should be written as the closed path integral of the canonical momentum; (ii) for the case of the gravitational WKB problem, there is a time-like 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 ordinary quantum mechanical WKB calculation.

8 pages, double column, 2 figures. Pedagogical article on Unruh radiation accepted for publication in AJP

References in corpus (13)

• Fermions Tunnelling from Black Holes
• Temporal contribution to gravitational WKB-like calculations
• Subtleties in the quasi-classical calculation of Hawking radiation
• Hawking black body spectrum from tunneling mechanism
• Thermal radiation of various gravitational backgrounds
• Problems with Tunneling of Thin Shells from Black Holes
• On the relation between Unruh and Sokolov--Ternov effects
• Detection of acceleration radiation in a Bose-Einstein condensate
• Particle decay in de Sitter spacetime via quantum tunneling
• Hawking Radiation as Quantum Tunneling in Rindler Coordinate
• On the physical meaning of the Unruh effect
• Decay of the cosmological constant by Hawking radiation as quantum tunneling
• A Brief Editorial on de Sitter Radiation via Tunneling

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• Black Hole Radiation with Modified Dispersion Relation in Tunneling Paradigm: Static Frame
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• Hawking radiation of E<m massive particles in the tunneling formalism
• On tunneling across horizons
• Classical and Quantum Aspects of Particle Propagation in External Gravitational Fields
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• Particle creation: Schwinger + Unruh + Hawking
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• Unruh thermalization, gluon condensation and freeze-out
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