极大超引力下旋转极值黑洞的广义Couch-Torrence对称性
Generalised Couch-Torrence Symmetry for Rotating Extremal Black Holes in Maximal Supergravity
摘要：
极端的Reissner-Nordström黑洞具有共形反演对称性，在这种对称性中，度规在径向坐标的反演和共形重标度的结合下被映射到自身。在旋转推广中，考奇和托伦斯指出，克尔-纽曼度规不再表现出共形反演对称性，但在无质量克莱因-戈登方程的分离中产生的径向方程允许依赖于模式的反演对称性，其中反演半径取决于模式的能量和方位角动量。最近的研究表明，STU超引力的静态4电荷极值黑洞承认共形反演对称性的推广，其中共形反演度规是同一个4电荷黑洞家族的成员，但具有变换的电荷。在本文中，我们研究进一步概括这些反演对称性，在一般类极端STU超引力黑洞。对于旋转的黑洞，再次无质量的克莱因-戈登方程是可分离的，我们表明，与四个电荷的例子表现出的沙发-托伦斯对称性的径向方程的概括。现在，就像在静态特化的共形反演中一样，径向方程的反演将其映射到具有变换的电荷的旋转黑洞的径向方程。我们还研究了反演变换的极端BPS STU黑洞携带8个电荷（4电加4磁）的一般情况下，并认为，类似的概括的反演对称性存在的静态和旋转的情况下。
英文摘要：
The extremal Reissner-Nordström black hole admits a conformal inversion symmetry, in which the metric is mapped into itself under an inversion of the radial coordinate combined with a conformal rescaling. In the rotating generalisation, Couch and Torrence showed that the Kerr-Newman metric no longer exhibits a conformal inversion symmetry, but the radial equation arising in the separation of the massless Klein-Gordon equation admits a mode-dependent inversion symmetry, where the radius of inversion depends upon the energy and azimuthal angular momentum of the mode. It was more recently shown that the static 4-charge extremal black holes of STU supergravity admit a generalisation of the conformal inversion symmetry, in which the conformally-inverted metric is a member of the same 4-charge black hole family but with transformed charges. In this paper we study further generalisations of these inversion symmetries, within the general class of extremal STU supergravity black holes. For the rotating black holes, where again the massless Klein-Gordon equation is separable, we show that examples with four electric charges exhibit a generalisation of the Couch-Torrence symmetry of the radial equation. Now, as in the conformal inversion of the static specialisations, the inversion of the radial equation maps it to the radial equation for a rotating black hole with transformed electric charges. We also study the inversion transformations for the general case of extremal BPS STU black holes carrying eight charges (4 electric plus 4 magnetic), and argue that analogous generalisations of the inversion symmetries exist both for the static and the rotating cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
