Gravitational Wave Signatures from Periodic Orbits around a Non--commutative Schwarzschild Black Hole
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 Θ/M2<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.
Versions
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BibTeX
@misc{heidari2026gravitational,
title = {{Gravitational Wave Signatures from Periodic Orbits around a Non--commutative Schwarzschild Black Hole}},
author = {N. Heidari and A. A. Araújo Filho and I. P. Lobo and V. B. Bezerra},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.26182},
eprint = {2606.26182},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26182},
}
RIS
TY - UNPB
TI - Gravitational Wave Signatures from Periodic Orbits around a Non--commutative Schwarzschild Black Hole
AU - N. Heidari
AU - A. A. Araújo Filho
AU - I. P. Lobo
AU - V. B. Bezerra
PY - 2026
DA - 2026/06/24
PB - arXiv
DO - 10.48550/arxiv.2606.26182
UR - https://arxiv.org/abs/2606.26182
AB - 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 Θ/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.
ER -