A Swampland-modified Hod bound for charged black holes with exotic matter

Abstract In this paper, we study the quasinormal modes (QNMs) of a charged black hole in the presence of both quintessence and a cloud of strings by using the Padé-averaged higher-order WKB approximation method. We investigate the effect of the quintessence parameter α and the cloud of strings parameter λ on stability as well as the oscillation frequency of perturbations. The validity of Hod’s conjecture, which relates quasinormal frequencies to the black hole temperature, is tested throughout the physically allowed parameter space. Our results show that both the effective potential and the decay rate of perturbations depend on the value of α and λ, leading to either enhancement or suppression of the conditions required to satisfy Hod’s bound. Furthermore, we discuss how these parameters modify the black hole shadow and the corresponding energy emission rate, proving correlations with observable signatures. Finally, we establish the connection with the Swampland Distance Conjecture by expressing the Hawking temperature in terms of the scalar field excursion. Our analysis leads to a modified Hod bound and identifies a region of parameter space in which both the modified Hod bound and the Swampland constraints are simultaneously satisfied, ensuring consistency between black hole thermodynamics, observational properties, and quantum gravity constraints.