Physical aspects of stationary axisymmetric vacuum spacetimes given by exact solutions of the Einstein equations are discussed via ray tracing. A detailed study of the spacetime generated by a disk of counter-rotating dust is presented. The spacetime is given in explicit form in terms of hyperelliptic theta functions. The numerical approach to ray tracing is set up for general stationary axisymmetric spacetimes and tested at the well-studied example of the Kerr solution. Similar features as in the case of a rotating black hole, are explored in the case of a dust disk. The effect of the central redshift varying between a Newtonian disk and the ultrarelativistic disk, where the exterior of the disk can be interpreted as the extreme Kerr solution, and the transition from a single component disk to a static disk is explored. Frame dragging, as well as photon spheres, are discussed.

中文翻译：

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使用光线追踪方法可视化反向旋转的灰尘盘


通过光线追迹讨论了由爱因斯坦方程的精确解给出的静止轴对称真空时空的物理方面。对反向旋转尘埃盘产生的时空进行了详细研究。时空以超椭圆 theta 函数的显式形式给出。射线追踪的数值方法是针对一般静止轴对称时空建立的，并在经过充分研究的克尔解示例中进行了测试。在尘埃盘的情况下也探索了与旋转黑洞类似的特征。牛顿盘和超相对论盘之间中心红移的影响不同，其中盘的外部可以解释为极端克尔解，并探讨了从单组分盘到静态盘的转变。讨论了框架拖动以及光子球。