The Kerr/CFT correspondence is a possible route to gain insight into the quantum theory of gravity in the near-horizon region of a Kerr black hole via a dual holographic conformal field theory (CFT). Predictions of the black hole entropy, scattering cross section and the quasinormal modes from the dual holographic CFT corroborate this proposed correspondence. More recently, it has been suggested that quantum gravitational effects in the near-horizon region of a black hole may drastically modify the classical general relativistic description, leading to potential observable consequences. In this paper, we study the absorption cross section and quasinormal modes of a horizonless Kerr-like exotic compact object (ECO) in the dual CFT picture. Our analysis suggests that the near-horizon quantum modifications of the black hole can be understood as finite size and/or finite $N$ effects in the dual CFT. Signature of the near-horizon modification to a black hole geometry manifests itself as delayed echoes in the ringdown (i.e., the postmerger phase) of a binary black hole coalescence. From our dual CFT analysis we show how the length of the circle, on which the dual CFT lives, must be related to the echo time-delay that depends on the position of the near-horizon quantum structure. We further derive the reflectivity of the ECO membrane in terms of the CFT modular parameters, showing that it takes the Boltzmann form.

中文翻译：

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Kerr / CFT对应中的回声

Kerr / CFT对应关系是通过双重全息共形场理论（CFT）深入了解Kerr黑洞近地平线区域中引力量子理论的一种可能途径。对偶全息CFT的黑洞熵，散射截面和准正态模的预测证实了这一拟议的对应关系。最近，有人提出，黑洞近地平线区域内的量子引力效应可能会极大地改变经典的广义相对论描述，从而导致潜在的可观测结果。在本文中，我们研究了双CFT图像中无水平Kerr状​​奇异压缩物体（ECO）的吸收截面和准正交模式。$ñ$双CFT中的效果。对黑洞几何体的近视水平修改的签名将其本身显示为二进制黑洞合并的衰荡（即合并后阶段）中的延迟回波。从我们的双重CFT分析中，我们可以看出存在双重CFT的圆的长度必须如何与回波时间延迟相关，回波时间延迟取决于近水平量子结构的位置。我们根据CFT模块化参数进一步推导了ECO膜的反射率，表明它采用了玻尔兹曼形式。