A Localized Axisymmetric Solution of the Hilbert-Einstein Equations for Spacetime Without Mass Sources
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Usually, the Hilbert-Einstein equations are considered for systems with mass-energy sources, and if one were to reduce the mass-parameter towards zero, the spacetime curvature would also diminish towards zero. However, in systems without mass-energy sources, the spacetime may locally exist as non-flat. We present a novel result—a localized axisymmetric solution of nonlinear GR equations for such massless systems—and provide step-by-step derivation for the solution.