论文标题
曲率，光子球和黑洞阴影
Curvatures, Photon Spheres and Black Hole Shadows
论文作者
论文摘要
在最近的工作PRD 106，L021501（2022）中，提出了一种新的几何方法，以获得光子球（圆形光子轨道）和黑洞阴影半径。在这种方法中，在黑洞空位的光学几何形状中，使用测量曲率和高斯曲率确定光子球和黑洞阴影半径。但是，PRD 106，L021501（2022）中的计算仅限于静态和球形对称黑洞的子类，带有时空度量$ g_ {tt} \ cdot g_ {rr} = -1 $，$ g_ g_ {fime $ g_ {ϕ} = r^{2} \ sin^{2}θ$。在这项工作中，我们将这种方法扩展到更一般的球形对称黑洞（带有空间度量$ ds^{2} = g_ {tt} dt} dt^{2}+g_ {rr}此外，可以证明，基于测试颗粒的有效势能，我们来自几何方法的结果完全等同于常规方法的结果。
In a recent work PRD 106, L021501 (2022), a new geometric approach is proposed to obtain the photon sphere (circular photon orbit) and the black hole shadow radius. In this approach, photon spheres and the black hole shadow radius are determined using geodesic curvature and Gaussian curvature in the optical geometry of black hole spacetimes. However, the calculations in PRD 106, L021501 (2022) only restricted to a subclass of static and spherically symmetric black holes with spacetime metric $g_{tt} \cdot g_{rr}=-1$, $g_{θθ}=r^{2}$ and $g_{ϕϕ}=r^{2}\sin^{2}θ$. In this work, we extend this approach to more general spherically symmetric black holes (with spacetime metric $ds^{2}=g_{tt}dt^{2}+g_{rr}dr^{2}+g_{θθ}dθ^{2}+g_{ϕϕ}dϕ^{2}$). Furthermore, it can be proved that our results from the geometric approach are completely equivalent to those from conventional approach based on effective potentials of test particles.
