Estabilidade De Buracos Negros Dilatônicos - Martins, Ébano Vitor Lopes (2024)
This thesis focuses on the stability analysis of static black holes within the framework of the Einstein-Maxwell-dilaton (EMd) theory. Our investigation involves deriving master equations that govern perturbations, encompassing different modes of odd and even parity. We establish criteria for assessing the stability of black holes using the theory of self-adjoint operators. Furthermore, we extend our analysis through the implementation of numerical simulations aimed at obtaining the temporal evolution of equations governing perturbations, thereby corroborating our analysis based on the theory of self-adjoint operators. We explore the superradiant instability, demonstrating that the unstable modes lead to instability if there is a potential well outside the horizon where these modes remain confined.