Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter

TL;DR

This paper investigates the causal structure and quasinormal modes of Schwarzschild-de Sitter spacetime, revealing insights into late-time correlator singularities, holographic complexity, and the switchback effect through shock wave perturbations.

Contribution

It provides a detailed analysis of quasinormal mode frequencies and the switchback effect in SdS, incorporating boundary conditions and complex geodesics for arbitrary black hole masses.

Findings

Identification of critical times indicating correlator singularities

Relation of critical time to diverging holographic complexity

Calculation of switchback delay with shock wave perturbations

Abstract

We study the causal structure of Schwarzschild-de Sitter (SdS), including shock wave perturbations, in $D>3$ using reflected null ray trajectories, either through the interior black hole or the exterior de Sitter region. Specifically, we compute the quasinormal mode frequencies in the eikonal, high-frequency, limit, by identifying the `critical time', for arbitrary values of the black hole mass. We emphasize the important role of the static sphere proper time normalization and related boundary conditions. The computed critical times indicate the presence of singularities in the late-time, large mass, scalar field correlator in SdS, which should be resolved by introducing complex geodesics consistent with interior black hole and exterior de Sitter effective thermofield double states. In addition we relate the critical time to a diverging holographic complexity observable and compute the `switchback' delay by adding a pair of shock wave perturbations for arbitrary values of the mass of the black hole.