Gravitational redshift cannot be represented by any finite set of smooth frequency modes, and the corrected finite-mode description is a Gaussian quantum channel built from a unitary dilation of the non-unitary compression.
Redshifts and Killing Vectors
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Courses in introductory special and general relativity have increasingly become part of the curriculum for upper-level undergraduate physics majors and master's degree candidates. One of the topics rarely discussed is symmetry, particularly in the theory of general relativity. The principal tool for its study is the Killing vector. We provide an elementary introduction to the concept of a Killing vector field, its properties, and as an example of its utility apply these ideas to the rigorous determination of gravitational and cosmological redshifts.
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Gravitational redshift as a quantum channel: modeling the effects of gravitational redshift in quantum optics
Gravitational redshift cannot be represented by any finite set of smooth frequency modes, and the corrected finite-mode description is a Gaussian quantum channel built from a unitary dilation of the non-unitary compression.