Harmonic coordinates satisfy the condition
 |
(1) |
or equivalently,
 |
(2) |
It is always possible to choose such a system. Using the d'Alembertian,
 |
(3) |
But since 
for harmonic coordinates, the result is a generalization of the harmonic equation
 |
(4) |
to
 |
(5) |
See also
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References
Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: Wiley, 1972.
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Cite this as:
Weisstein, Eric W. "Harmonic Coordinates." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HarmonicCoordinates.html