Black holes in Starobinsky-Bel-Robinson Gravity and the breakdown of quasinormal modes/null geodesics correspondence

TL;DR

This paper investigates the stability and quasinormal mode behavior of black holes in Starobinsky-Bel-Robinson Gravity, revealing instability conditions, peculiar spectral features, and the breakdown of the quasinormal modes/null geodesics correspondence.

Contribution

It demonstrates the instability of scalar perturbations in this gravity model and shows the failure of the high-frequency quasinormal modes and null geodesics correspondence.

Findings

Scalar field perturbations are unstable unless coupling is small.

Quasinormal spectrum exhibits two-stage ringing with different dominant modes.

The high-frequency quasinormal modes do not fully match null geodesic characteristics.

Abstract

We show that perturbations of a scalar field in the background of the black hole obtained with the Starobinsky-Bel-Robinson Gravity is unstable unless the dimensionless coupling $\beta$ describing the compactification of M-theory is small enough. In the sector of stability quasinormal spectrum show peculiar behavior both in the frequency and time domains: the ringing consists of two stages where two different modes dominate. The WKB method does not reproduce part of the spectrum including the fundamental mode, which is responsible for the first stage of the ringing. As a result, the correspondence between the high frequency quasinormal modes and characteristics of the null geodesics reproduces only one branch of the eikonal spectrum. The frequencies are obtained with the help of three methods (Frobenius, WKB and time-domain integration) with excellent agreement among them.