[论文解读] Electric charge of black holes: Is it really always negligible?

Michal Zajaček, Arman Tursunov|arXiv (Cornell University)|Apr 9, 2019

Astrophysical Phenomena and Observations被引用 28

一句话总结

本文挑战了天体物理学模型中黑洞电荷可忽略的普遍假设。研究表明，即使电荷较小——例如银河系中心黑洞的电荷约为10⁸ C——也能对带电粒子（如宇宙射线）产生比引力强达16倍的电磁力，显著改变粒子动力学和ISCO位置，因此电荷在高能天体物理学和多信使天文学中不应被忽略。

ABSTRACT

We discuss the problem of the third black hole parameter, an electric charge. While the mass and the spin of black holes are frequently considered in the majority of publications, the charge is often neglected and implicitly set identically to zero. However, both classical and relativistic processes can lead to a small non-zero charge of black holes. When dealing with neutral particles and photons, zero charge is a good approximation. On the other hand, even a small charge can significantly influence the motion of charged particles, in particular cosmic rays, in the vicinity of black holes. Therefore, we stress that more attention should be paid to the problem of a black-hole charge and hence, it should not be neglected a priori, as it is done in most astrophysical studies nowadays. The paper looks at the problem of the black-hole charge mainly from the astrophysical point of view, which is complemented by a few historical as well as philosophical notes when relevant. In particular, we show that a cosmic ray or in general elementary charged particles passing a non-neutral black hole can experience an electromagnetic force as much as sixteen times the gravitational force for the mass of the Galactic centre black hole and its charge being seventeen orders of magnitude less than the extremal value (calculated for a proton). Furthermore, a Kerr-Newman rotating black hole with the maximum likely charge of 1 Coulomb per solar mass can have the position of its innermost stable circular orbit (ISCO) moved by both rotation and charge in ways that can enhance or partly cancel each other, putting the ISCO not far from the gravitational radius or out at more than 6 gravitational radii. An interpretation of X-ray radiation from near the ISCO of a black hole in X-ray binaries is then no longer unique.

研究动机与目标

• 挑战天体物理学中黑洞电荷可忽略且可设为零的常见假设。
• 研究黑洞通过热力学或相对论机制获得非零电荷的物理机制，包括热平衡和Wald的感应机制。
• 评估非零黑洞电荷对带电粒子（特别是宇宙射线）运动的可观测影响。
• 考察黑洞电荷如何影响最内层稳定圆轨道（ISCO）的位置，从而复杂化X射线辐射的解释。
• 主张在建模黑洞吸积和能量提取过程时，电荷应被视为非平凡参数。

提出的方法

• 利用保守引力场和电场中的麦克斯韦-玻尔兹曼分布，分析宏观天体的电荷质量比平衡，推导出Qeq/M• ≈ 76.9 C/M⊙。
• 应用Wald于1974年提出的机制，模拟在外部磁场中旋转黑洞的电荷感应，其中Q• = 2a•M•Bext。
• 使用Kerr-Newman度规建模带电旋转黑洞的时空结构，并计算带电测试粒子的ISCO。
• 比较黑洞附近质子和电子所受静电与引力的比值，显示当Q• ≈ 10⁸ C且M• ≈ 4×10⁶ M⊙时，Felstat/Fgrav ≈ 16。
• 构建ISCO位置图（图1），作为电子和质子的黑洞电荷函数，显示ISCO最大可移动9个引力半径。
• 评估自旋、电荷和磁场在移动ISCO中的退化关系，导致X射线光曲线解释不唯一。

实验结果

研究问题

• RQ1 黑洞是否可通过热力学或相对论机制获得非零电荷？
• RQ2 在电荷较小但非零的情况下，带电粒子（如质子）在黑洞附近的电磁力与引力相比有多强？
• RQ3 电荷在多大程度上能模拟或改变黑洞自旋对ISCO位置的影响？
• RQ4 在X射线双星或银河系中心观测到的ISCO是否可唯一归因于自旋，还是电荷或磁场也可能导致？
• RQ5 非零黑洞电荷对超高能宇宙射线起源有何影响？

主要发现

• 在电荷为10⁸ C、质量为4×10⁶ M⊙的黑洞附近，质子所受静电力比引力强16倍。
• 电荷为3.3×10⁵ C的黑洞可使电子的ISCO移动至9个引力半径，其效果类似于逆行自旋。
• 对于质子，负电荷-6.0×10⁸ C或正电荷+5.07×10⁹ C可同样将ISCO推至9rg。
• 周围核区磁场的存在也会移动ISCO，与电荷和自旋在ISCO解释中形成退化。
• 即使电荷很小，仅电荷本身即可使非旋转黑洞的ISCO从6rg位移到9rg。
• Blandford-Znajek机制通过电磁场提取旋转能量，其驱动力来自黑洞电荷，表明电荷对喷流形成至关重要。