(Quasi-)normal modes of rotating black holes and new solitons in Einstein-Gauss-Bonnet

TL;DR

This paper studies the (quasi-)normal modes of rotating black holes and new solitons in five-dimensional Einstein-Gauss-Bonnet gravity, revealing their spectral properties, stability features, and the existence of solutions with non-trivial torsion.

Contribution

It provides the first detailed analysis of scalar mode spectra for these black holes and solitons, including analytical and numerical results, and introduces solutions with non-trivial torsion in this context.

Findings

Imaginary parts of static black hole modes are negative, indicating stability.

Rotating black holes exhibit modes with imaginary parts approaching zero near extremality.

Both black holes and solitons can have non-trivial torsion, leading to new solution branches.

Abstract

In this paper, we analyze the scalar field (quasi-)normal modes of recently derived rotating black holes within the framework of Einstein-Gauss-Bonnet theory at the Chern-Simons point in five dimensions. We also examine the mode spectrum of these probes on new static gravitational solitons. These solitons, featuring a regular center, are constructed from static black holes with gravitational hair via a double analytic continuation. By imposing ingoing boundary conditions at the horizons of rotating black holes, ensuring regularity at the soliton centers, and imposing Dirichlet boundary conditions at infinity, we obtain numerical spectra for the rotating black holes and solitons. For static black holes, we demonstrate analytically that the imaginary part of the mode frequencies is negative. Our analysis of the massless Klein-Gordon equation on five-dimensional geometries reveals an infinite family of gaped, massive three-dimensional Klein-Gordon fields, despite the presence of a non-compact extended direction. For the static solitons, the frequencies are real and non-equispaced, whereas in the rotating black holes, counter-rotating modes are absorbed more quickly, and the imaginary part of the co-rotating modes approaches zero as extremality is approached. Additionally, we show that both the rotating black holes and solitons can be equipped with non-trivial torsion, leading to a novel branch of solutions.