Higher spin mode stability for STU black hole backgrounds

This work studies mode stability of an STU black hole with four pairwise equal $\rm{U(1)}$ charges in four spacetime dimensions. We investigate bosonic perturbations 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\c{s} (2016) to prove the absence of unstable modes that solve the torsion-modified Dirac equation appropriate for this black hole background.