Decoupling and non-decoupling dynamics of large D black holes

TL;DR

This paper analyzes the spectrum of quasinormal modes of large D Schwarzschild black holes, revealing two classes of modes with distinct properties and frequencies, and confirms findings with numerical results even at D=4.

Contribution

It provides a detailed classification of decoupled and non-decoupled quasinormal modes in large D black holes and matches analytical results with numerical data.

Findings

Most modes are non-decoupled, straddling near-horizon and asymptotic zones.

A small set of decoupled modes are normalizable and specific to each black hole.

Analytical frequencies agree well with numerical calculations, even at D=4.

Abstract

The limit of large number of dimensions localizes the gravitational field of a black hole in a well-defined region near the horizon. The perturbative dynamics of the black hole can then be characterized in terms of states in the near-horizon geometry. We investigate this by computing the spectrum of quasinormal modes of the Schwarzschild black hole in the 1/D expansion, which we find splits into two classes. Most modes are non-decoupled modes: non-normalizable states of the near-horizon geometry that straddle between the near-horizon zone and the asymptotic zone. They have frequency of order D/r_0 (with r_0 the horizon radius), and are also present in a large class of other black holes. There also exist a much smaller number of decoupled modes: normalizable states of the near-horizon geometry that are strongly suppressed in the asymptotic region. They have frequency of order 1/r_0, and are specific of each black hole. Our results for their frequencies are in excellent agreement with numerical calculations, in some cases even in D=4.