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arXiv · 2606.26182

Gravitational Wave Signatures from Periodic Orbits around a Non--commutative Schwarzschild Black Hole

N. Heidari·A. A. Araújo Filho·I. P. Lobo·V. B. Bezerra
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Abstract

In this work, we investigate massive particle motion and the gravitational wave emission generated by periodic trajectories around a non--commutative \textit{Schwarzschild} black hole sourced by a Lorentzian matter distribution. We analyze the effective potential, the marginally bound orbit, and the innermost stable circular orbit, showing that non--commutative corrections shift these characteristic orbits toward smaller radii and reduce their corresponding angular momenta. The allowed region in the $(E, L)$ plane is also displaced toward lower values, favoring more tightly bound configurations. Periodic trajectories are classified through the rational parameter $q$, which relates the radial and azimuthal frequencies. For a fixed orbital topology, increasing the non--commutative parameter lowers the energy required to produce the orbit and results in more compact zoom--whirl configurations. Small deviations from the periodic energies are also shown to generate precessional drift. From the periastron advance of the S2 star around Sgr~A$^*$, we obtain the preliminary bound $\Theta/M^{2}<0.014$. Finally, using the adiabatic and numerical kludge approximations, we compute the gravitational wave polarizations and find phase shifts and an overall enhancement of the amplitude.

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N. Heidari, A. A. Araújo Filho, I. P. Lobo, V. B. Bezerra. 2026-06-24. Gravitational Wave Signatures from Periodic Orbits around a Non--commutative Schwarzschild Black Hole. https://arxiv.org/abs/2606.26182

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