论文标题
在加速黑洞的时空中，灯光般的大地测量学和重力镜头
Lightlike Geodesics and Gravitational Lensing in the Spacetime of an Accelerating Black Hole
论文作者
论文摘要
C-metric是爱因斯坦真空场方程的解决方案，描述了加速黑洞的加速。在本文中，我们讨论了光线的传播以及该指标中产生的镜头特征。我们首先使用椭圆形积分和Jacobi椭圆函数求解了光明的测量方程。然后，我们将静态观察者固定在C-metric的外部通信区域中，并引入正顺式四分法，以使用观察者天体上的纬度宽度坐标在观察者位置终止的光线的方向。在此参数化中，我们重新绘制了阴影的角度半径，我们制定了镜头方程，并得出了红移和光线的行进时间。我们讨论了我们的理论结果与检测C-Metric所描述的加速黑洞的相关性，并将其与非加速黑洞区分开。
The C-metric is a solution to Einstein's vacuum field equation that describes an accelerating black hole. In this paper we discuss the propagation of light rays and the resulting lensing features in this metric. We first solve the lightlike geodesic equation using elliptic integrals and Jacobi elliptic functions. Then we fix a static observer in the region of outer communication of the C-metric and introduce an orthonormal tetrad to parameterise the directions of the light rays ending at the position of the observer using latitude-longitude coordinates on the observer's celestial sphere. In this parameterisation we rederive the angular radius of the shadow, we formulate a lens equation, and we derive the redshift and the travel time of light rays. We discuss the relevance of our theoretical results for detecting accelerating black holes described by the C-metric and for distinguishing them from non-accelerating black holes.
