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arXiv 2603.03033gr-qc
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Carrollian相关函数在黑洞扰动理论中的应用

Carrollian correlators in black hole perturbation theory

School of Physics, Huazhong University of Science and Technology(华中科技大学物理学院)

Jiang Long, Zhan-Jia Qu, Hong-Yang Xiao

AI总结:

本文研究了Carrollian相关函数在黑洞扰动理论中的应用,揭示了其与无质量散射的关系,并提出了两种经典方程的双重描述。

摘要:

在本文中,我们澄清了两点Carrollian相关函数与黑洞背景中无质量散射之间的关系。结果表明,每个渐近平坦时空的null边界中存在两种类型的Carrollian相关函数。从$\mathscr I^-$到$\mathscr I^+$的相关函数应通过减去平坦空间的类比进行正则化,并且是无质量散射反射振幅的位置空间版本。另一方面,从$\mathscr I^-$到未来视界$\mathcal H^+$的相关函数在平坦空间中不存在,且是传输振幅的位置空间版本。Carrollian相关函数的极点由从$\mathscr I^-$到$\mathscr I^+$或$\mathcal H^+$的null测地线决定,并且定义了Carrollian空间中的两种经典方程。这些方程建立了Shapiro时间延迟与光束偏转角之间的关系,并应被理解为准正常模式(QNMs)和格林函数分支割的双重描述。我们发现,对于小偏转角,从$\mathscr I^-$到$\mathscr I^+/\mathcal H^+$的相关函数的时间延迟包含对数/二次行为。另一方面,当偏转角较大时,对于两种相关函数,时间延迟始终以线性方式增加。

英文摘要:

In this note, we clarify the relationship between the two-point Carrollian correlator and massless scattering in black hole background. It turns out that there are two kinds of Carrollian correlators at the null boundaries of each asymptotically flat spacetime. The correlator from $\mathscr I^-$ to $\mathscr I^+$ should be regularized by subtracting the flat space analog, and it is the position space version of the reflection amplitude of massless scattering. On the other hand, the correlator from $\mathscr I^-$ to the future horizon $\mathcal H^+$ is absent in flat space, and it is the position space version of the transmission amplitude. The poles of the Carrollian correlators are governed by the null geodesics from $\mathscr I^-$ to $\mathscr I^+$ or $\mathcal H^+$, and they define two kinds of classical equations in Carrollian space. These equations establish the relationship between the Shapiro time delay and the deflection angle for light rays and should be understood as the dual descriptions of the quasinormal modes (QNMs) and the branch cut of the Green's function. We find that the time delay contains a logarithmic/quadratic behavior for the correlator from $\mathscr I^-$ to $\mathscr I^+/\mathcal H^+$ for small deflection angles. On the other hand, the time delay is always increasing linearly for both correlators when the deflection angle is large.

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