Hyperbolic reduction of the Weyl–Lanczos equations

What is it about?

The Weyl-Lanczos equation gives the free gravitational field in terms of a three rank tensor potential, called the Lanczos potential. In this respect it resembles how the electromagnetic field tensor may be uniquely determined by a vector potential. We show that this equation may be put on a much simpler form analogous to the electric and magnetic decomposition of the Maxwell equations, thus making the Weyl-Lanczos equation more readily accessible for mathematical analysis and physical interpretation.

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Photo by Dynamic Wang on Unsplash

Photo by Dynamic Wang on Unsplash

Why is it important?

The Weyl-Lanczos equation suggest that the Lanczos potential is of primary importance in the study of gravitational radiation. But the complicated nature of the equation makes it inconvenient to work with and difficult to interpret the physical meaning of the potential. Hence, it is of interest to cast the equation on a form which is more accessible for interpretation and analysis.