Thin accretion-disc transfer functions in the q-metric spacetime: quadrupolar lensing signatures
Abstract
We study geometrically thin equatorial disc images in the static, axisymmetric q-metric spacetime using backward ray tracing. The Schwarzschild solution is recovered at q=0; for the nonzero deformations considered here, r=2M is a curvature singularity rather than an event horizon. For a distant nearly face-on observer, we construct the first three equatorial transfer functions rm(b;q). In the {Schwarzschild} limit, the resolved third-crossing interval contains the critical impact parameter b=3√3M. As q increases from −0.3 to $0.3$, the branch center shifts from b3,c/M≃3.716 to $6.702$. In units of the physical monopole mass ℳ=(1+q)M, it instead decreases from b3,c/ℳ≃5.309 to $5.156$. Much of the displacement in metric-parameter units therefore reflects the changing monopole scale. At fixed ℳ, the inclined first-intersection maps show that the contour dimensions increase with q, with larger relative changes near the inner disc. A prescribed power-law emissivity and relativistic frequency-shift weighting yield direct images whose integrated flux differs from the Schwarzschild value by at most 2.4%. Between the endpoint models, the horizontal median-flux position increases by 8.8% and the interquartile width by 14.5%. Within this emission prescription, the residual deformation dependence appears mainly as a displacement and broadening of the brightness distribution. Higher-order radiative contributions are not included.
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BibTeX
@misc{toktarbay2026thin,
title = {{Thin accretion-disc transfer functions in the q-metric spacetime: quadrupolar lensing signatures}},
author = {Saken Toktarbay and Manas Khassanov and Aray Muratkhan and Zhantay Muratkhan and Aliya Taukenova and Hernando Quevedo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07259},
eprint = {2609.07259},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07259},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Thin accretion-disc transfer functions in the q-metric spacetime: quadrupolar lensing signatures
AU - Saken Toktarbay
AU - Manas Khassanov
AU - Aray Muratkhan
AU - Zhantay Muratkhan
AU - Aliya Taukenova
AU - Hernando Quevedo
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07259
UR - https://arxiv.org/abs/2609.07259
AB - We study geometrically thin equatorial disc images in the static, axisymmetric q-metric spacetime using backward ray tracing. The Schwarzschild solution is recovered at q=0; for the nonzero deformations considered here, r=2M is a curvature singularity rather than an event horizon. For a distant nearly face-on observer, we construct the first three equatorial transfer functions r_m(b;q). In the {Schwarzschild} limit, the resolved third-crossing interval contains the critical impact parameter b=3√3M. As q increases from −0.3 to $0.3$, the branch center shifts from b_3,c/M≃3.716 to $6.702$. In units of the physical monopole mass ℳ=(1+q)M, it instead decreases from b_3,c/ℳ≃5.309 to $5.156$. Much of the displacement in metric-parameter units therefore reflects the changing monopole scale. At fixed ℳ, the inclined first-intersection maps show that the contour dimensions increase with q, with larger relative changes near the inner disc. A prescribed power-law emissivity and relativistic frequency-shift weighting yield direct images whose integrated flux differs from the Schwarzschild value by at most 2.4%. Between the endpoint models, the horizontal median-flux position increases by 8.8% and the interquartile width by 14.5%. Within this emission prescription, the residual deformation dependence appears mainly as a displacement and broadening of the brightness distribution. Higher-order radiative contributions are not included.
ER -