Adapted harmonic coordinates

Physics

Scientific paper

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Scientific paper

We obtain the necessary and sufficient conditions that a timelike congruence has to satisfy to admit three independent adapted harmonic coordinates of space, proving in the process that if it does then these coordinates are unique up to a linear transformation with constant coefficients. As a particular example we prove that irrotational pure Born (i.e. not Killing) congruences never admit a system of adapted harmonic coordinates of space.

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