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

Understand

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.