On a zero-gravity limit of the Kerr--Newman spacetimes and their electromagnetic fields
On a zero-gravity limit of the Kerr--Newman spacetimes and their electromagnetic fields
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论克尔-纽曼时空及其电磁场的零重力极限
DOI：
10.1063/1.4915290
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
A. Tahvildar
中科院分区：
文献类型：
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作者：
A. Tahvildar
我们讨论了极大解析扩展Kerr-Newman电真空时空(用Boyer-Lindquist坐标表示)的消失极限。我们研究了在这个极限下出现的拓扑非平凡时空，证明了它是由两个平坦的Minkowski时空粘合在一个类时的实心圆柱上组成的。当G0$时，Kerr-Newman时空的电磁场收敛到麦克斯韦方程的非平凡解。我们展示了如何通过求解麦克斯韦方程来获得这些场，其中奇异源只支持在时空的类空间切片中的一个圆上。这些源不会遭受任何在先前试图解释拓扑简单的Minkowski时空上的克尔-纽曼场时发现的其他源的病态之苦。我们刻画了这些源的奇异行为，并证明了Kerr-Newman静电势和磁流函数是在环奇点具有相同爆破行为的所有函数中Maxwell方程的唯一解。
We discuss the limit of vanishing $G$ (Newton's constant of universal gravitation) of the maximal analytically extended Kerr--Newman electrovacuum spacetimes {represented in Boyer--Lindquist coordinates}. We investigate the topologically nontrivial spacetime emerging in this limit and show that it consists of two copies of flat Minkowski spacetime glued at a timelike solid cylinder. As $G\to 0$, the electromagnetic fields of the Kerr-Newman spacetimes converge to nontrivial solutions of Maxwell's equations on this background spacetime. We show how to obtain these fields by solving Maxwell's equations with singular sources supported only on a circle in a spacelike slice of the spacetime. These sources do not suffer from any of the pathologies that plague the alternate sources found in previous attempts to interpret the Kerr--Newman fields on the topologically simple Minkowski spacetime. We characterize the singular behavior of these sources and prove that the Kerr-Newman electrostatic potential and magnetic stream function are the unique solutions of the Maxwell equations among all functions that have the same blow-up behavior at the ring singularity.