Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-12-16
Class.Quant.Grav.27:015012,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages (minor changes in reference [30])
Scientific paper
10.1088/0264-9381/27/1/015012
We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in modifying both the ADecM linear operator with highest order derivative and ADecM polynomials. We specialize in the case of a 4$\times$4 nonlinear MDE along with a scalar one describing stationary cylindrically symmetric metrics in quadratic 5-dimensional GR, derive some of their properties using ADecM and construct the \textit{most general unique power series solutions}. However, because of the constraint imposed on the MDE by the scalar one, the series solutions terminate in closed forms exhausting all possible solutions.
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