A black hole embedded within a bright, optically thin emitting region imprints a nearly circular "shadow" on its image, corresponding to the observer's line-of-sight into the black hole. The shadow boundary depends on the black hole's mass and spin, providing an observable signature of both properties via high resolution images. However, standard expressions for the shadow boundary are most naturally parametrized by Boyer-Lindquist radii rather than by image coordinates. We explore simple, approximate parameterizations for the shadow boundary using ellipses and a family of curves known as limacons. We demonstrate that these curves provide excellent and efficient approximations for all black hole spins and inclinations. In particular, we show that the two parameters of the limacon naturally account for the three primary shadow deformations resulting from mass and spin: size, displacement, and asymmetry. These curves are convenient for parametric model fitting directly to interferometric data, they reveal the degeneracies expected when estimating black hole properties from images with practical measurement limitations, and they provide a natural framework for parametric tests of the Kerr metric using black hole images.
Shadows and Polarization Images of a Four-dimensional Gauss-Bonnet Black Hole Irradiated by a Thick Accretion Disk
College of Physics and Electronic Engineering, Chongqing Normal University（重庆师范大学物理与电子工程学院）；School of Material Science and Engineering, Chongqing Jiaotong University（重庆交通大学材料科学与工程学院）；Department of Mathematics, School of Science, University of Management and Technology（管理技术大学理学院数学系）；Department of Mathematics, COMSATS University Islamabad, Lahore Campus（科摩特斯伊斯兰堡大学拉合尔校区数学系）
Using horizon shadows to distinguish a black hole and a white hole
College of Science, Northeast Forestry University（东北林业大学理学院）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学学院）
A coordinate-independent characterization of a black hole shadow
目前正在进行一项大规模的国际努力，以评估银河系中心人马座A $^*$（Sgr A $^*$）致密源的无线电发射中是否存在阴影。如果被探测到，这个阴影将提供黑洞存在的第一个直接证据，并证明Sgr A $^*$是一个超大质量黑洞。此外，阴影的形状可以用来了解事件视界附近的极端引力，并确定哪种引力理论更好地描述了观测结果。到目前为止，阴影的数学描述使用了许多简化的假设，这些假设不太可能被真实的观测数据所满足。在这里，我们提供了一个一般的形式主义来描述的阴影作为一个任意的极曲线表示的勒让德展开。我们的形式主义不假定任何知识的属性的阴影，例如，其中心的位置，并提供了一些路线来表征扭曲的曲线相对于参考圆。这些扭曲可以通过分析相同数据的不同团队以独立于坐标的方式实现。我们表明，新的形式主义提供了一个准确和强大的描述嘈杂的观测数据，与以前的方法相比，失真的测量具有较小的误差方差。
