Ladder symmetries of black holes. Implications for love numbers and no-hair theorems
Ladder symmetries of black holes. Implications for love numbers and no-hair theorems
复制标题
黑洞的阶梯对称性。
DOI：
10.1088/1475-7516/2022/01/032
复制
发表时间：
2022
影响因子：
6.4
通讯作者：
Solomon, Adam R.
中科院分区：
文献类型：
--
作者：
Hui, Lam;Joyce, Austin;Penco, Riccardo;Santoni, Luca;Solomon, Adam R.
众所周知，广义相对论中渐近平坦的黑洞具有消失的静态、保守的潮汐响应。我们证明这是控制黑洞周围静态(自旋0，1，2)微扰的线性实现的对称性的结果。对称性有一个几何起源：在标量情况下，它们来自一个维度缩减的黑洞时空的(E)ad等距。在对称性的下面是一个梯形结构，它可以用来构造整个解的塔，并得出它们的一般性质：(1)随着半径衰减的解自发地破坏对称性，并且必须在地平线发散；(2)在地平线上规则的解尊重对称性，并且采取随半径增长的有限多项式的形式。综合起来，这两个性质意味着静态响应系数--尤其是洛夫数--消失了。此外，性质(1)与不存在线状(微扰)毛发的黑洞是一致的。我们还讨论了这些对称性在黑洞的有效点粒子描述中的表现，明确地表明，对于标量探测器来说，为了保持对称性，与非平凡的潮汐反应和标量头发相关的世界线耦合必须消失。
It is well known that asymptotically flat black holes in general relativity have a vanishing static, conservative tidal response. We show that this is a result of linearly realized symmetries governing static (spin 0, 1, 2) perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E) AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions, and derive their general properties:(1) solutions that decay with radius spontaneously break the symmetries, and must diverge at the horizon;(2) solutions regular at the horizon respect the symmetries, and take the form of a finite polynomial that grows with radius. Taken together, these two properties imply that static response coefficients—and in particular Love numbers—vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probes the worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.
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