Higher spin mode stability for STU black hole backgrounds

This article studies mode stability of a four-dimensional rotating black hole with four pairwise equal U(1) charges derived in the framework of supergravity or the low energy string theory which is known now as STU black hole. We investigate bosonic perturbations in a proposed equation of the Teukolsky type for probe fields of different spins through the transformation technique devised by Whiting in 1989. Finally, we introduce connection relations inspired by the work of Duzta {{s}} {s}{} [Phys. Rev. D 94, 044025 (2016) ] to prove the absence of unstable modes that solve the torsion-modified Dirac equation appropriate for this black hole background.