标题： 一个对偶关系：全局单极子和纹理 显示英文标题

标题： A duality relation : global monopole and texture

摘要： 我们解决了整个引力场；即，将黎曼曲率分解为其电部分和磁部分。 一般来说，真空爱因斯坦方程在主动电部分和被动电部分之间是对称的。 然而结果表明，施瓦茨希尔德解，即唯一的球对称真空解，可以通过一个稍微更一般的方程来表征，该方程并不对称。 然后，对偶变换，意味着主动部分和被动部分的互换，将把施瓦茨希尔德粒子与具有全局单极子电荷的粒子联系起来。 也就是说，这两个是彼此的对偶。 进一步发现，平直时空与无质量全局单极子和全局纹理时空是对偶的。 显示英文摘要

摘要： We resolve the entire gravitational field;i.e. the Riemann curvature into its electric and magnetic parts. In general, the vacuum Einstein equation is symmetric in active and passive electric parts. However it turns out that the Schwarzschild solution, which is the unique spherically symmetric vacuum solutions can be characterised by a slightly more general equation which is not symmetric. Then the duality transformation, implying interchange of active and passive parts will relate the Schwarzschlid particle with the one with global monopole charge. That is the two are dual of each-other. It further turns out that flat spacetime is dual to massless global monopole and global texture spacetimes.