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arXiv 2402.07574hep-thgr-qc
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高维球对称黑洞的 $p$-形式与引力扰动的 Love 数和 Love 对称性

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

Panagiotis Charalambous

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64+3 pages, 5 figures
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AI总结：

本文研究了高维球对称黑洞的 $p$-形式与引力扰动，解析提取了静态 Love 数与耗散数，发现 Love 对称性可由表示论解释 Love 数的消失，并探讨了其在弦论校正下的几何涌现条件。

摘要：

已知四维渐近平坦、孤立的一般相对论性黑洞的静态 Love 数恒为零。Love 对称性假说提出，这种消失可通过近域区域中增强的 $\text{SL}(2,\mathbb{R})$（“Love”）对称性的出现所导出的选择定则来解释；更具体地说，是黑洞扰动属于该近域 $\text{SL}(2,\mathbb{R})$ 对称性的最高权表示这一事实，而非 Love 对称性本身的存在，输出了相应 Love 数的消失。在高维时空中，针对 Schwarzschild-Tangherlini 黑洞的标量、电磁和引力扰动，也曾报道过关于黑洞响应问题的一些“神奇零点”塔。在此，我们通过补充 Schwarzschild-Tangherlini 黑洞的 $p$-形式扰动来扩展这些结果。我们进一步解析地提取了高维 Reissner-Nordström 黑洞的自旋-$0$ 标量和自旋-$2$ 张量型潮汐扰动的静态 Love 数以及主导阶耗散数。我们发现，即使对于广义相对论中高维球对称黑洞的这些更高自旋扰动，Love 对称性依然存在，且静态 Love 数的消失可由表示论论证来刻画。有趣的是，这些近域 $\text{SL}(2,\mathbb{R})$ 结构可扩展为 Witt 代数。我们的设定也允许研究一般引力理论中静态球对称黑洞的 $p$-形式响应问题。我们对存在弦论校正情况下的一些黑洞进行了显式计算，并研究在何种几何条件下 Love 对称性会在近域中出现。

英文摘要：

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-Nordström 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.

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