标题： 广义相对论中的方向裸奇点 显示英文标题

标题： Directional naked singularity in general relativity

摘要： 我们考虑一个静态、轴对称且渐近平直的爱因斯坦真空方程精确解，称为伽马度规。 该度规由两个常参数 $m$ 和 $\gamma$ 特征化。 我们发现与此度规相关的总能量为 $m \gamma$。 考虑到总能量为正，我们研究了在此度规中的曲率奇异性 $r=2m$ （其中 $r$ 是径向坐标）的性质。 对于 $\gamma < 1$，这种奇点不仅在 $\theta = 0$ 上，而且在 $\theta = \pi /2$ 上也全局可见。 然而，对于 $\gamma > 1$，尽管在 $\theta =\pi/2$ 上全局裸露，但在 $\theta = 0$ 上却不可见（甚至局部也不可见）。 因此，这展示了 $\gamma > 1$ 的“方向性裸露”。 这可能对天体物理学有影响。 显示英文摘要

摘要： We consider a static, axially symmetric, and asymptotically flat exact solution of the Einstein vacuum equations, known as the gamma metric. This is characterized by two constant parameters $m$ and $\gamma$. We find that the total energy associated with this metric is $m \gamma$. Considering the total energy to be positive, we investigate the nature of a curvature singularity $r=2m$ ($r$ is the radial coordinate) in this metric. For $\gamma < 1$, this singularity is globally visible along $\theta = 0$ as well as $\theta = \pi /2$. However, for $\gamma > 1$, this singularity is though globally naked along $\theta =\pi/2$, it is not visible (even locally) along $\theta = 0$. Thus, this exhibits ``directional nakedness'' for $\gamma > 1$. This could have implications for astrophysics.