论文标题
Selberg Zeta warped广告功能$ _3 $黑洞
A Selberg zeta function for warped AdS$_3$ black holes
论文作者
论文摘要
Selberg Zeta功能和跟踪公式是用于计算双曲商空位上的动力学操作器光谱和准模式的强大工具。在本文中，我们通过为扭曲的广告构建Selberg Zeta功能$ _3 $黑洞，将这种形式主义扩展到非纤维化商。我们还考虑了所谓的自动划分解决方案，这些解决方案与接近野马的极端凯尔有关。我们在Zeta函数零和扭曲广告上的准模式之间建立了一个地图，$ _3 $黑洞背景。在此过程中，我们使用一种涉及共形坐标的方法及其对称结构的标量拉普拉斯式的对称结构来构建双曲线半空间度量标准的翘曲版本，据我们所知，这是新的，并且可能具有自己的有趣应用程序，我们可以描述。最后，我们讨论了这项工作的几个未来方向，例如在我们考虑的商空间上计算1循环的决定因素（控制量子校正），以及将此处提出的形式主义调整为更通用的Orbifolds。
The Selberg zeta function and trace formula are powerful tools used to calculate kinetic operator spectra and quasinormal modes on hyperbolic quotient spacetimes. In this article, we extend this formalism to non-hyperbolic quotients by constructing a Selberg zeta function for warped AdS$_3$ black holes. We also consider the so-called self-dual solutions, which are of interest in connection to near-horizon extremal Kerr. We establish a map between the zeta function zeroes and the quasinormal modes on warped AdS$_3$ black hole backgrounds. In the process, we use a method involving conformal coordinates and the symmetry structure of the scalar Laplacian to construct a warped version of the hyperbolic half-space metric, which to our knowledge is new and may have interesting applications of its own, which we describe. We end by discussing several future directions for this work, such as computing 1-loop determinants (which govern quantum corrections) on the quotient spacetimes we consider, as well as adapting the formalism presented here to more generic orbifolds.
