Reconstruction of Noether Symmetries and Their Application to the Derivation of Killing Vector Fields

Emiliano Aguilar-Rivas, Ricardo à guila-Gómez, Ernesto Urenda-Cázares, Armando Gallegos and Miriam Bocardo-Gaspar

Journal of Applied Mathematics, 2026, vol. 2026, 1-12

Abstract: This work introduces a novel variational framework for the reconstruction of Noether symmetries for N-parameter point transformations. We demonstrate that the problem of finding symmetries can be reduced to the analysis of a single parameter via a linear differential operator Dχ. Although the relationship between isometries and Noether symmetries is a cornerstone of general relativity, we present a distinct methodological approach to derive the partial differential equations of Killing vector fields. Our framework utilizes the arc length functional and pseudo-Riemannian metric concepts while deliberately circumventing the direct use of the Lie derivative and the Levi-Civita connection. The results confirm that variational invariance conditions recover the classical Killing equations exactly. Furthermore, the analysis of modified actions (gauge function F≠0) demonstrates that the admissible isometries are strictly static with respect to the parameterization, proving the robustness of the proposed methodology in finding spacetime symmetries without relying on traditional geometric tools.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:7581213

DOI: 10.1155/jama/7581213

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