sentences:  The essential motivation for introducing harmonic coordinate systems is that the metric tensor is especially smooth when written in these coordinate systems.Harmonic coordinates are characterized in terms of the Christoffel symbols by means of the relation
  and indeed, for any coordinate system at all,
  Harmonic coordinates always exist (locally), a result which follows easily from standard results on the existence and regularity of solutions of elliptic partial differential equations.In particular, the equation
  has a solution in a ball around any given point "p", such that "u""j"("p") and formula_6 are all prescribed.