Developed Adomian method for quadratic Kaluza-Klein relativity

Understand

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.