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- Title
Efficient trace-free decomposition of symmetric tensors of arbitrary rank.
- Authors
Toth, Viktor T.; Turyshev, Slava G.
- Abstract
Symmetric trace-free tensors are used in many areas of physics, including electromagnetism, relativistic celestial mechanics and geodesy, as well as in the study of gravitational radiation and gravitational lensing. Their use allows integration of the relevant wave propagation equations to arbitrary order. We present an improved iterative method for the trace-free decomposition of symmetric tensors of arbitrary rank. The method can be used both in coordinate-free symbolic derivations using a computer algebra system and in numerical modeling. We obtain a closed-form representation of the trace-free decomposition in arbitrary dimensions. To demonstrate the results, we compute the coordinate combinations representing the symmetric trace-free (STF) mass multipole moments for rank 5 through 8, not readily available in the literature.
- Subjects
RELATIVISTIC mechanics; GRAVITATIONAL waves; GEODETIC astronomy; GRAVITATIONAL lenses; DECOMPOSITION method
- Publication
International Journal of Geometric Methods in Modern Physics, 2022, Vol 19, Issue 13, p1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887822502012