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Symmetric trace-free tensors are used in many areas of physics, includingelectromagnetism, relativistic celestial mechanics and geodesy, as well as inthe study of gravitational radiation and gravitational lensing. Their useallows integration of the relevant wave propagation equations to arbitraryorder. We present an improved iterative method for the trace-free decompositionof symmetric tensors of arbitrary rank. The method can be used both incoordinate-free symbolic derivations using a computer algebra system and innumerical modeling. We obtain a closed-form representation of the trace-freedecomposition in arbitrary dimensions. To demonstrate the results, we computethe coordinate combinations representing the symmetric trace-free (STF) massmultipole moments for rank 5 through 8, not readily available in theliterature.

Efficient trace-free decomposition of symmetric tensors of arbitrary rank