We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w| 0) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit w→1, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state p=ρ.

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在广义相对论中旋转类梅尔文宇宙和虫洞

我们找到了爱因斯坦-麦克斯韦方程的一系列精确解，用于旋转完美流体的圆柱对称分布，状态方程 p=wρ (|w| 0) 描述了不包含对称轴的可穿越虫洞几何形状。与梅尔文的解决方案不同，那些有旋转和磁场的解决方案不能是真空的，需要电流。虫洞解决方案允许与喉咙两侧的平坦空间区域匹配，从而形成圆柱形虫洞配置，对于居住在平坦或弱弯曲空间部分的远处观察者来说可能是可见的。The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, 因此，它形成了广义相对论中无幻影虫洞模型的新例子。在极限 w→1 下，磁场趋于零，虫洞模型趋向于先前得到的模型，其中重力源是刚性物质，状态方程为 p=ρ。