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

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.