Black holes are said to have no hair because all of their multipole moments can be expressed in terms of just their mass, charge and spin angular momentum. The recent discovery of approximately equation-of-state-independent relations among certain multipole moments in neutron stars suggests that they are also approximately bald. We here explore the yet unknown origin for this universality. First, we investigate which region of the neutron star's interior and of the equation of state is most responsible for the universality. We find that the universal relation between the moment of inertia and the quadrupole moment is dominated by the star's outer-core, a shell of width (50-95)% of the total radius, which corresponds to the density range $(10^{14}$-$10^{15})$g/cm$^3$. Second, we study the impact on the universality of approximating stellar isodensity contours as self-similar ellipsoids. An analytical calculation in the Newtonian limit reveals that the shape of the ellipsoids does not affect the universal relations, but relaxing the self-similarity assumption can completely destroy it. Third, we investigate the eccentricity profiles of rotating relativistic stars and find that the ellipticity is roughly constant, with variations of roughly (20-30)% in the region that matters to the universal relations. Fourth, we repeat the above analysis for non-compact, regular stars and find that the ellipticity is not constant, with variations that easily exceed 100% and universality is lost. These findings suggest that universality arises as an emergent approximate symmetry: as one flows in the stellar-structure phase space from non-compact star region to the relativistic star region, the eccentricity variation inside stars decreases, leading to approximate self-similarity in their isodensity contours, which then leads to the universal behavior observed in their exterior multipole moments.
Compact body in a tidal environment: New types of relativistic Love numbers, and a post-Newtonian operational definition for tidally induced multipole moments
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。
Universal Closed Form for Dynamical Love Numbers of Black Holes
Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·鲍姆克理论物理研究所物理学与天文学系）
Nonlinear Relativistic Tidal Response of Neutron Stars
Dipartimento di Fisica, “Sapienza” Università di Roma & Sezione INFN Roma1（罗马大学物理系与INFN罗马第一分部）；Department of Physics, Center for Theoretical Physics, Columbia University（哥伦比亚大学理论物理中心物理系）；Université Paris Cité, CNRS, Astroparticule et Cosmologie（巴黎西岱大学、法国国家科学研究中心粒子物理与宇宙学）；Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique（巴黎萨克雷大学、法国国家科学研究中心、法国原子能和替代能源委员会理论物理研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
