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arXiv · 2607.24654

Test-particle dynamics in a noncommutative deformation of Einstein-Rosen waves

Diego Henrique Carvalho dos Santos·José André Lourenço·Davi C. Rodrigues·Etevaldo dos Santos Costa Filho
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Abstract

We investigate phenomenological effects induced by a noncommutative deformation of Einstein--Rosen gravitational-waves within the framework of the Riemannian geometry of noncommutative surfaces developed by Chaichian et al. Considering a noncommutative structure between the radial and axial coordinates, we study perturbatively the motion of nonrelativistic test particles in the corresponding deformed geometry. We show that the deformation generates a coupling between the radial and longitudinal sectors, while the radial dynamics remains unaffected by the noncommutative deformation at the perturbative order considered. The induced longitudinal response is governed by a spectrally weighted functional of the gravitational-wave profile, implying that longitudinal observables depend on higher-order spectral moments than their commutative radial counterparts. As a consequence, noncommutative effects exhibit enhanced sensitivity to the ultraviolet structure of the gravitational configuration. We analyze separately monochromatic Einstein--Rosen waves and the localized Weber--Wheeler pulse. In the monochromatic case, the noncommutative correction induces a quasi-periodic longitudinal motion, whereas for the Weber--Wheeler pulse it produces an impulsive longitudinal response analogous to a gravitational velocity memory effect. In addition, we derive an explicit analytical expression in commutative General Relativity for the residual radial velocity generated by the Weber--Wheeler pulse at large radial distances in the perturbative regime.

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Diego Henrique Carvalho dos Santos, José André Lourenço, Davi C. Rodrigues, Etevaldo dos Santos Costa Filho. 2026-07-27. Test-particle dynamics in a noncommutative deformation of Einstein-Rosen waves. https://arxiv.org/abs/2607.24654

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