One of the macroscopically measurable effects of gravity is the tidal deformability of astrophysical objects, which can be quantified by their tidal Love numbers. For planets and stars, these numbers measure the resistance of their material against the tidal forces, and the resulting contribution to their gravitational multipole moments. According to general relativity, deformed black holes, instead, show no addition to their gravitational multipole moments, and all of their Love numbers are zero. In this paper we explore different configurations of nonrotating compact and ultracompact stars to bridge the compactness gap between black holes and neutron stars and calculate their Love number $k_2$. We calculate $k_2$ for the first time for uniform density ultracompact stars with mass $M$ and radius $R$ beyond the Buchdahl limit (compactness $C = M/R > 4/9$), and we find that $k_2 \to 0^+$ as $C \to 1/2$, i.e., the Schwarzschild black hole limit. Our results provide insight on the zero tidal deformability limit and we use current constraints on the binary tidal deformability $\tilde{\Lambda}$ from GW170817 (and future upper limits from binary black hole mergers) to propose tests of alternative models.

中文翻译：

---

爱在哪里？黑洞紧致极限中的潮汐变形能力

重力的宏观可测量影响之一是天体物理物体的潮汐变形能力，可以通过它们的潮汐洛夫数来量化。对于行星和恒星，这些数字衡量了它们的材料对潮汐力的抵抗力，以及由此产生的对其引力多极矩的贡献。相反，根据广义相对论，变形黑洞的引力多极矩没有增加，它们的所有洛夫数都为零。在本文中，我们探索了非旋转致密星和超致密星的不同配置，以弥合黑洞和中子星之间的致密性差距，并计算它们的洛夫数 $k_2$。我们首次计算了质量为 M$ 且半径为 R$ 的均匀密度超致密星的 $k_2$ 超出了布赫达尔极限（致密性 $C = M/R > 4/9$），我们发现 $k_2 \ to 0^+$ as $C \to 1/2$，即史瓦西黑洞极限。我们的结果提供了对零潮汐变形极限的洞察，我们使用来自 GW170817 的二元潮汐变形能力 $\tilde{\Lambda}$ 的当前约束（以及来自二元黑洞合并的未来上限）来提出替代模型的测试。