标题： 爱数与爱对称性：关于$p$形式的高维球对称黑洞的引力扰动 显示英文标题

标题： Love numbers and Love symmetries for $p$-form and gravitational perturbations of higher-dimensional spherically symmetric black holes

摘要： 四维渐近平坦、孤立的广义相对论黑洞的静态Love数已知完全为零。 Love对称性猜想表明，这种消失可以通过近区区域增强的$\text{SL}(2,\mathbb{R})$ （“Love”）对称性的出现所导致的选择规则来解释；更具体地说，是黑洞扰动属于该近区$\text{SL}(2,\mathbb{R})$对称性的最高权表示，而非Love对称性的存在本身，导致了相应Love数的消失。 在更高维度时，对于Schwarzschild-Tangherlini黑洞的标量、电磁和引力扰动，也报告了一些关于黑洞响应问题的魔法零序列。 在这里，我们通过补充Schwarzschild-Tangherlini黑洞的$p$形式扰动，扩展了这些结果。 此外，我们解析地提取了高维Reissner-Nordström黑洞的静止Love数以及与自旋$0$标量和自旋$2$张量型潮汐扰动相关的主导耗散数。 我们发现，即使对于广义相对论中更高自旋的高维球对称黑洞的扰动，Love对称性仍然存在，并且静止Love数的消失可以通过表示论论证来捕捉。 有趣的是，这些近区$\text{SL}(2,\mathbb{R})$结构获得了Witt代数的扩展。 我们的设定还允许研究一般重力理论中静态球对称黑洞的$p$形响应问题。 我们在存在弦理论修正的一些黑洞上进行了显式计算，并研究了在近区条件下Love对称性出现的几何条件。 显示英文摘要

摘要： The static Love numbers of four-dimensional asymptotically flat, isolated, general-relativistic black holes are known to be identically vanishing. The Love symmetry proposal suggests that such vanishings are addressed by selection rules following from the emergence of an enhanced $\text{SL}(2,\mathbb{R})$ ("Love") symmetry in the near-zone region; more specifically, it is the fact that the black hole perturbations belong to a highest-weight representation of this near-zone $\text{SL}(2,\mathbb{R})$ symmetry, rather than the existence of the Love symmetry itself, that outputs the vanishings of the corresponding Love numbers. In higher spacetime dimensions, some towers of magic zeroes with regards to the black hole response problem have also been reported for scalar, electromagnetic and gravitational perturbations of the Schwarzschild-Tangherlini black hole. Here, we extend these results by supplementing with $p$-form perturbations of the Schwarzschild-Tangherlini black hole. We furthermore analytically extract the static Love numbers and the leading order dissipation numbers associated with spin-$0$ scalar and spin-$2$ tensor-type tidal perturbations of the higher-dimensional Reissner-Nordstr\"om black hole. We find that Love symmetries exist and that the vanishings of the static Love numbers are captured by representation theory arguments even for these higher spin perturbations of the higher-dimensional spherically symmetric black holes of General Relativity. Interestingly, these near-zone $\text{SL}(2,\mathbb{R})$ structures acquire extensions to Witt algebras. Our setup allows to also study the $p$-form response problem of a static spherically symmetric black hole in a generic theory of gravity. We perform explicit computations for some black holes in the presence of string-theoretic corrections and investigate under what geometric conditions Love symmetries emerge in the near-zone.