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2018

Novel matter coupling in general relativity via canonical transformation

Aoki, Katsuki, Lin, Chunshan, Mukohyama, Shinji

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We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity.

Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples to the canonically transformed gravitational field.
We find that a naive matter coupling to the transformed field leads to the appearance of an extra mode in the phase space, rendering the theory inconsistent.
We then find a consistent and novel way of matter coupling: after imposing a gauge fixing condition, a matter field can minimally couple to gravity without generating an unwanted extra mode.

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