Similarity Solutions of the Einstein-Maxwell equations with 1 Killing Vector
Elliot Fischer
TL;DR
This paper introduces new similarity variables for the Einstein-Maxwell equations with one Killing vector, reducing complex PDEs to ODEs and deriving new solutions that extend previous work with two Killing vectors.
Contribution
The paper develops novel similarity variables for Einstein-Maxwell equations with one Killing vector, enabling reduction to ODEs and generating new solutions.
Findings
New similarity variables reduce PDEs to ODEs
Derived explicit solutions for Einstein-Maxwell equations
Extended previous solutions from two to one Killing vector
Abstract
New similarity variables are introduced for the Einstein - Maxwell equations with one Killing vector that reduce the non-linear partial differential equations in three independent variables to ordinary differential equations. These similarity variables are the extensions of those previously found for the Einstein-Maxwell equations with two Killing vectors. The resulting equations are then solved, providing new solutions of the Einstein - Maxwell equations with one Killing Vector.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Numerical methods for differential equations · Nonlinear Waves and Solitons