Developed Adomian method for quadratic Kaluza-Klein relativity

Abstract

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.

17 pages (minor changes in reference [30])

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Cited by in corpus (4)

• Light paths of normal and phantom Einstein-Maxwell-dilaton black holes
• Rotating normal and phantom Einstein--Maxwell--dilaton black holes: Geodesic analysis
• Computation of the general relativistic perihelion precession and of light deflection via the Laplace-Adomian Decomposition Method
• Series solution of the time-dependent Schrödinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method