论文标题
Schwarzschild黑洞周围赤道发射环的高阶图像的形状：极曲线的分析描述
Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves
论文作者
论文摘要
可以预期，可以在未来观察结果中发现的黑洞的更详细图像中检测到高阶光子环。这些环是黑洞周围发光物质的镜头图像，并由围绕它的光子形成。在本文中，我们成功地以最方便的应用形式得出了高阶环形状的分析表达式：极性坐标中曲线的显式方程。该公式描述了圆形环的高阶图像的明显形状，其在Schwarzschild Black Hole周围的给定半径是遥远的观察者，并具有任意倾斜度。对于派生，使用重力挠度的强挠度极限。我们的公式是射线轨迹数值计算的简单有效替代方案，主要应用于研究$ n = 2 $和$ n = 3 $ photon环的形状。
Higher-order photon rings can be expected to be detected in a more detailed image of the black hole found in future observations. These rings are lensed images of the luminous matter surrounding the black hole and are formed by photons that loop around it. In this paper we have succeeded to derive an analytical expression for the shape of the higher-order rings in the form that is most convenient for application: the explicit equation of the curve in polar coordinates. The formula describes the apparent shape of the higher-order image of the circular ring with the given radius around Schwarzschild black hole as viewed by distant observer with an arbitrary inclination. For the derivation, the strong deflection limit of the gravitational deflection is used. Our formula is a simple and efficient alternative to the numerical calculation of ray trajectories, with the main application to studying the shape of $n=2$ and $n=3$ photon rings.
