It was shown in a recent paper [J. Math. Phys. 60, 102502 (2019)] that slowly lowering an electric charge into a Schwarzschild-Tangherlini (ST) black hole endows the final state with electric multipole fields, which implies the final state geometry is not Reissner-Nordström-Tangherlini in nature. This conclusion departs from the four-dimensional case in which the no-hair theorem (NHT) requires the final state to be a Reissner-Nordström black hole. To better understand this discrepancy clearly requires a deeper understanding of the origin of the multipole hair in the higher-dimensional case. In this paper, we advance the conjecture that charged, static, and asymptotically-flat higher-dimensional black holes can acquire electric multipole hair only after they form. This supposition derives from studying the asymptotic behavior of the field of a multipole charge onto which a massive and hyperspherical shell with an exterior ST geometry is collapsing. In the mathematical limit as the shell approaches its ST radius, we find that the multipole fields (except the monopole) vanish. This implies that the only information of an arbitrary (but finite) charge distribution inside the collapsing shell that is available to an asymptotic observer is the total electric charge. Our results yield considerable insight into how higher-dimensional black holes acquire electric multipole hair, and also imply that, in four dimensions, the fadeaway of multipole moments during gravitational collapse is not strictly because of the NHT.
Motion of extended fluid bodies in the Newtonian limit of $f(R)$ gravity
Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science and Technology, Guangxi University（广西大学物理科学与技术学院相对论天体物理重点实验室）；Guangxi Center for Mathematical Research, Guangxi University（广西大学广西数学研究中心）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
Tidally induced multipole moments of a nonrotating black hole vanish to all post-Newtonian orders
黑洞的潮汐勒夫数消失，这通常被认为意味着黑洞的潮汐诱导多极矩也消失了。在这些陈述之间建立联系的一个障碍是，当物体受到相互引力相互作用时，单个物体的多极矩在广义相对论中没有定义。在以前的出版物[Phys. Rev. D 103，064023（2021）]中，我提出了这样一种观点，即当相互作用足够弱，可以用后牛顿展开来描述时，可以定义各个多极矩。在这种观点中，一个紧凑的身体被视为遥远的具有多极结构的后牛顿物体，多极矩可以与身体的爱数有关。我扩大这一观点，并证明，所有静态的，潮汐诱导，质量多极矩的非旋转黑洞消失的所有后牛顿秩序。证明依赖于爱因斯坦-麦克斯韦方程组的微扰解，该方程组描述了一个放置在带电黑洞中的带电粒子。粒子与黑洞之间的引力吸引被静电斥力平衡，系统处于平衡态。粒子为黑洞提供了一个潮汐环境，在这种环境下多极矩消失。我认为，消失是强大的，并适用于所有缓慢变化的潮汐环境。黑洞的电荷可以尽可能的小（尽管不完全为零）;通过连续性，电中性黑洞的多极矩将继续消失。
Constraining the electric charges of some astronomical bodies in Reissner-Nordstrom spacetimes and generic r^-2-type power-law potentials from orbital motions
