Killing矢量场引起的原初磁场生成
Primordial Magnetogenesis from Killing Vector Fields
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中文总结 AI 辅助
本文推广Papapetrou定理，证明Killing矢量场协变导数在非真空背景也满足麦克斯韦方程，提出Killing电磁场与电磁流概念，推导其宇宙磁场上限，并揭示Schwarzschild时空在弱场下转化为Reissner-Nordström度规，关联“无电荷的电荷”计划。
中文摘要 AI 辅助
Papapetrou证明了Killing矢量场的协变导数在真空中满足麦克斯韦方程组。我们将Papapetrou的结果加以推广，证明在非真空背景下，如果允许存在纯几何起源的电磁流，则Killing矢量场的协变导数同样满足麦克斯韦方程组。我们假设每一个Killing矢量场都会产生一个物理电磁场，并且在非真空背景下还会产生一个物理电磁流——以下分别称为Killing电磁场和Killing电磁流。我们证明了平坦FLRW宇宙的Killing电磁场包含一个Killing磁场和一个旋转Killing电场；我们推导出Killing磁场的上限，并发现该上限与当前宇宙磁场的上限一致。我们证明了Schwarzschild时空的类时Killing矢量会产生一个径向Killing电场。我们还证明，在弱场区域——且远离物质分布时——径向Killing电场的反作用会将Schwarzschild度规改变为Reissner-Nordström度规；我们的计算得出了Wald结果的逆命题。接下来，借鉴Rainich关于Rainich-Riemann流形的研究，我们讨论了物理电磁场如何从几何中产生的病因学问题；我们还论证了平坦FLRW时空的Killing电场的探测可能在当前实验可及范围之内。最后，我们讨论了Killing电磁流以及前述Schwarzschild时空向Reissner-Nordström时空的转化，与Misner和Wheeler实现“无电荷的电荷”计划的相关性。
英文摘要
Papapetrou showed that the covariant derivative of a Killing vector field satisfies Maxwell's equations in vacuum. We extend Papapetrou's result to show that the covariant derivative of a Killing vector field satisfies Maxwell's equations in non-vacuum backgrounds as well, if we allow electromagnetic currents of purely geometric origin. We postulate that every Killing vector field gives rise to a physical electromagnetic field and, in a non-vacuum background, a physical electromagnetic current---hereafter called Killing electromagnetic field and Killing electromagnetic current, respectively. We show that the Killing electromagnetic field of the flat FLRW universe comprises a Killing magnetic field and a rotational Killing electric field; we derive an upper bound on the Killing magnetic field and find that the upper bound is consistent with the current upper bound on the cosmic magnetic field. We show that the time-like Killing vector of the Schwarzschild spacetime gives rise to a radial Killing electric field. We also show that in the weak field regime---and far from the matter distribution---the back reaction of the radial Killing electric field changes the Schwarzschild metric to Reissner-Nordstr$\ddot{\mbox{o}}$m metric; our calculation yields the converse of Wald's result. Next, drawing upon Rainich's work on Rainich-Riemann manifolds, we discuss the etiological question of how a physical electromagnetic field can arise out of geometry; we also argue that detection of the Killing electric field of flat FLRW spacetime may be within current experimental reach. Finally, we discuss the relevance of Killing electromagnetic currents and the aforementioned transmutation of Schwarzschild spacetime to Reissner-Nordstrom spacetime, to Misner and Wheeler's program of realizing ``charge without charge''.
发表机构
- Purdue University（普渡大学）
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