论文标题
爱对称
Love symmetry
论文作者
论文摘要
Kerr-Newman Black Hole背景中无质量领域的扰动享受（``Love''）SL $（2，\ Mathbb {r}）$对称性在区域近似附近定义的适当定义。我们介绍了对这种对称性的详细研究，并展示了如何从SL $（2，\ Mathbb {r}）$表示理论中理解四个和更高维度的黑洞响应的复杂行为。特别是，四维黑洞的静态扰动属于最高权重sl $ \ left（2，\ mathbb {r} \ right）$表示。正是这种最高的重量属性迫使静态爱情数量消失。我们发现，爱对称性与极端黑洞的增强异构体密切相关。对于极端带电的球形对称（Reissner-Nordström）解决方案，这种关系是最简单的，其中，爱对称完全减少到近地平线广告$ _2 $喉咙的等距。为了旋转（Kerr-Newman）黑洞，一个导致考虑一个无限的sl $ \ left（2，\ mathbb {r} \ right）\ ltimes \ hat u（1）_ {\ mathcal {v}} $ symmetry的扩展。它包含三个物理上不同的亚词法：爱代数，近区代数附近的Starobinsky和近地平线代数，它们成为极限极限的Bardeen-Horowitz等轴测图。我们还讨论了爱对称性的其他方面，例如其发电机的几何含义，用于旋转的加权领域的几何含义，与无头发定理的联系，爱情数字的非确定性，其与（非超级）KERR/CFT的关系以及其存在于重力理论中的存在。
Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (``Love'') SL$(2,\mathbb{R})$ symmetry in the suitably defined near zone approximation. We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL$(2,\mathbb{R})$ representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL$\left(2,\mathbb{R}\right)$ representations. It is this highest weight property that forces the static Love numbers to vanish. We find that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. This relation is simplest for extremal charged spherically symmetric (Reissner-Nordström) solutions, where the Love symmetry exactly reduces to the isometry of the near horizon AdS$_2$ throat. For rotating (Kerr-Newman) black holes one is lead to consider an infinite-dimensional SL$\left(2,\mathbb{R}\right)\ltimes \hat U(1)_{\mathcal{V}}$ extension of the Love symmetry. It contains three physically distinct subalgebras: the Love algebra, the Starobinsky near zone algebra, and the near horizon algebra that becomes the Bardeen-Horowitz isometry in the extremal limit. We also discuss other aspects of the Love symmetry, such as the geometric meaning of its generators for spin weighted fields, connection to the no-hair theorems, non-renormalization of Love numbers, its relation to (non-extremal) Kerr/CFT correspondence and prospects of its existence in modified theories of gravity.
