Carrollian correlators in black hole perturbation theory

TL;DR

This paper explores the relationship between Carrollian correlators at black hole null boundaries and massless scattering, revealing their connection to classical light ray equations, quasinormal modes, and scattering amplitudes.

Contribution

It clarifies the dual roles of two types of Carrollian correlators in black hole spacetimes and their link to scattering amplitudes and classical geodesic equations.

Findings

Correlator from  to  relates to reflection amplitude.

Correlator from  to  horizon relates to transmission amplitude.

Time delay behaviors depend on deflection angle, showing logarithmic/quadratic or linear growth.

Abstract

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.