Solution of the Helmholtz equation for spin-2 fields
General Relativity and Quantum Cosmology
2007-05-23 v1
Abstract
The Helmholtz equation for symmetric, traceless, second-rank tensor fields in three-dimensional flat space is solved in spherical and cylindrical coordinates by separation of variables making use of the corresponding spin-weighted harmonics. It is shown that any symmetric, traceless, divergenceless second-rank tensor field that satisfies the Helmholtz equation can be expressed in terms of two scalar potentials that satisfy the Helmholtz equation. Two such expressions are given, which are adapted to the spherical or cylindrical coordinates. The application to the linearized Einstein theory is discussed.
Keywords
Cite
@article{arxiv.gr-qc/0305002,
title = {Solution of the Helmholtz equation for spin-2 fields},
author = {G. F. Torres del Castillo and J. E. Rojas Marcial},
journal= {arXiv preprint arXiv:gr-qc/0305002},
year = {2007}
}
Comments
13 pages, no figures. Paper already published in Revista Mexicana de Fisica