标题： 球对称的真空空间及其在广义相对论中的对偶性 显示英文标题

标题： Spherically symmetric empty space and its dual in general relativity

摘要： 在牛顿理论的精神下，我们根据静态观察者测量的能量密度以及零和类时凝聚体经历的收敛密度来表征广义相对论中的球对称真空空间。 结果表明，静态粒子周围的空空间完全由能量和零收敛密度的消失所确定。 与此条件的电引力对偶$^{1}$将是类时和零收敛密度的消失，这给出了代表具有全局单极电荷$^{2}$的施瓦茨希尔德黑洞或具有弦尘云$^{3}$的对偶真空解。 在这里，对偶性$^{1}$通过交换黎曼曲率的主动和被动电部分来定义，这相当于交换里奇张量和爱因斯坦张量。 这种对静态真空的有效表征适用于施瓦茨希尔德解和NUT解。 对空空间有效表征最显著的特点是它导致了新的对偶空间，该方法也可以应用于低维和高维空间。 显示英文摘要

摘要： In the spirit of the Newtonian theory, we characterize spherically symmetric empty space in general relativity in terms of energy density measured by a static observer and convergence density experienced by null and timelike congruences. It turns out that space surrounding a static particle is entirely specified by vanishing of energy and null convergence density. The electrograv-dual$^{1}$ to this condition would be vanishing of timelike and null convergence density which gives the dual-vacuum solution representing a Schwarzschild black hole with global monopole charge$^{2}$ or with cloud of string dust$^{3}$. Here the duality$^{1}$ is defined by interchange of active and passive electric parts of the Riemann curvature, which amounts to interchange of the Ricci and Einstein tensors. This effective characterization of stationary vacuum works for the Schwarzschild and NUT solutions. The most remarkable feature of the effective characterization of empty space is that it leads to new dual spaces and the method can also be applied to lower and higher dimensions.