发表机构
Al-Farabi Kazakh National University; Kazakh National Women’s Teacher Training University; Universidad Nacional Autónoma de México; Università di Roma “La Sapienza”（阿尔法拉比哈萨克国立大学; 哈萨克国立女子师范大学; 墨西哥国立自治大学; 罗马第一大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在q-度规时空中用反向光线追踪研究薄盘图像，构造转移函数，发现四极形变主要引起亮度分布位移和展宽，通量差异不超过2.4%。
AI 中文摘要
我们利用反向光线追踪研究了静态、轴对称q-度规时空中几何薄赤道盘图像。在$q=0$时恢复史瓦西解；对于此处考虑的非零形变，$r=2M$是曲率奇点而非事件视界。对于远处近乎正面的观测者，我们构造了前三个赤道转移函数$r_m(b;q)$。在史瓦西极限中，解析的第三交叉区间包含临界碰撞参数$b=3\sqrt{3}M$。当$q$从$-0.3$增加到$0.3$时，分支中心从$b_{3,c}/M\simeq3.716$移动到$6.702$。以物理单极质量$\mathcal M=(1+q)M$为单位，它反而从$b_{3,c}/\mathcal M\simeq5.309$减小到$5.156$。因此，在度规参数单位下的大部分位移反映了单极尺度的变化。在固定$\mathcal M$下，倾斜的第一交叉映射显示轮廓尺寸随$q$增加，且内盘附近相对变化更大。采用规定的幂律发射率和相对论频移加权，直接图像的总通量与史瓦西值的差异最多为$2.4\\%$。在端点模型之间，水平中值通量位置增加$8.8\\%$，四分位距宽度增加$14.5\\%$。在这种发射规定下，残余形变依赖性主要表现为亮度分布的位移和展宽。未包含高阶辐射贡献。
英文摘要
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 $b=3\sqrt{3}M$. As $q$ increases from $-0.3$ to $0.3$, the branch center shifts from $b_{3,c}/M\simeq3.716$ to $6.702$. In units of the physical monopole mass $\mathcal M=(1+q)M$, it instead decreases from $b_{3,c}/\mathcal M\simeq5.309$ to $5.156$. Much of the displacement in metric-parameter units therefore reflects the changing monopole scale. At fixed $\mathcal M$, 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.
Comments45 pages, 5 figures, 8 tables
