发表机构
Institució Catalana de Recerca i Estudis Avançats (ICREA); Universitat de Barcelona; Perimeter Institute for Theoretical Physics（加泰罗尼亚研究与高级研究所; 巴塞罗那大学; 理论物理前沿研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究黑洞-弦转变中潮汐可变形性，计算HP弦星在4、5、6维下多极矩ℓ=2、3、4的静态洛夫数，发现其响应非零且洛夫数随ℓ线性增长，为弦星特性提供潮汐特征。
AI 中文摘要
潮汐可变形性是探测致密天体结构的灵敏探针，在四维爱因斯坦引力中，黑洞的静态洛夫数（Love numbers）为零，表现出特殊的刚性。我们探究在黑洞-弦转变过程中，这种精细调谐的刚性会发生怎样的变化——在此转变中，相同的态有望被描述为弱耦合的自引力高度激发弦，即“弦星”。我们计算了霍罗维茨-波尔钦斯基（Horowitz-Polchinski, HP）弦星在D=4、5、6维下，多极矩ℓ=2、3、4对应的静态潮汐洛夫数。结果显示，所有情况下响应均非零，这与已有的α'修正黑洞结果一致，说明四维爱因斯坦引力的零洛夫结构在转变两侧均不成立。不过在弦侧，响应具有独特的多极结构：洛夫数随ℓ快速增长，我们通过解析推导证明，这种增长源于潮汐场的多极权重与卷绕凝聚体的指数尾部之间的竞争，最终在大多极数ℓ下，可变形性探测的径向尺度随ℓ线性增长。这为弦星的延展、无表面特性提供了直接的潮汐特征。我们还讨论了其与α'修正黑洞的对比，以及现有大多极数下微扰结果的局限性。
英文摘要
Tidal deformability provides a sensitive probe of the structure of compact objects, and black holes are exceptional in having vanishing static Love numbers in four-dimensional Einstein gravity. We ask what happens to this fine-tuned rigidity across the black hole-string transition, where the same states are expected to admit a weakly coupled description as a self-gravitating highly excited string, or "string star". We compute the static tidal Love numbers of the Horowitz-Polchinski (HP) string star for multipoles $\ell=2,3,4$ in $D=4,5,6$. The response is non-zero in all cases, as in the available $α'$-corrected black hole results, so the zero-Love structure of four-dimensional Einstein gravity does not survive on either side of the transition. On the string side, however, the response has a distinctive multipolar structure: the Love numbers grow rapidly with $\ell$, and we show analytically that this growth originates from the competition between the multipolar weight of the tidal field and the exponential tail of the winding condensate, with the result that the radial scale probed by the deformability grows linearly with $\ell$ at large multipole number. This provides a direct tidal signature of the extended, surface-less nature of the string star. We discuss the comparison with $α'$-corrected black holes and the limitations of the currently available perturbative results at large $\ell$.
Comments32 pages, 3 figures; v2: small improvements and refs added
