论文标题
Brill空数的重力镜头
Gravitational lensing in Brill spacetimes
论文作者
论文摘要
我们认为Brill Metric是爱因斯坦磁场方程的电动解决方案。这取决于三个参数，一个质量参数$ m $，一个螺母参数$ l $和电荷参数$ e $。如果电荷参数很小，则指标描述了一个黑洞。如果足够大，它描述了一个虫洞。我们确定了黑洞和虫洞中的相关镜头特征。特别是，我们为光子球，阴影的角度和偏转角度提供了公式。我们借助有效的潜力和嵌入图表来说明镜头特征。为此，我们利用了这样一个事实，即每个灯泡的大地测量都包含在（坐标）锥中，并且它是该锥体上riemannian光学指标的地球测量。通过高斯河网定理，光学度量的高斯曲率的符号决定了偏转角的符号。在虫洞的情况下，挠度角可能为负，这意味着光线从中心排出。
We consider the Brill metric which is an electrovacuum solution to Einstein's field equation. It depends on three parameters, a mass parameter $m$, a NUT parameter $l$ and a charge parameter $e$. If the charge parameter is small, the metric describes a black hole; if it is sufficiently big, it describes a wormhole. We determine the relevant lensing features both in the black-hole and in the wormhole case. In particular, we give formulas for the photon spheres, for the angular radius of the shadow and for the deflection angle. We illustrate the lensing features with the help of an effective potential and in terms of embedding diagrams. To that end we make use of the fact that each lightlike geodesic is contained in a (coordinate) cone and that it is a geodesic of a Riemannian optical metric on this cone. By the Gauss-Bonnet theorem, the sign of the Gaussian curvature of the optical metric determines the sign of the deflection angle. In the wormhole case the deflection angle may be negative which means that light rays are repelled from the center.
