A Novel KEER-SEN Solution Satisfying SO(2) Symmetry via Laurent Series Expansion

We propose a novel KEER-SEN solution satisfying the SO(2) symmetry group, derived using a Laurent series expansion technique. Building upon stationary Euclidean solutions to the vacuum Einstein equations and incorporating recent advances in generating stationary fields, our method integrates variation-of-constants and nonlinear superposition techniques. This approach provides new insights into axially symmetric gravitational fields, extends the Kerr-NUT solution framework, and unifies several classical methods. Detailed derivations, numerical simulations, and discussions of physical implications (including dilaton and axion effects) are presented. The expanded version includes a more extensive historical overview of axisymmetric solutions, a deeper discussion of the formalism behind Laurent series expansions in gravitational contexts, and an in-depth analysis of the physical significance of KEER-SEN solutions in modern theoretical and astrophysical research.