Aspectos quânticos e clássicos da instabilidade de campos fundamentais em espaços-tempos astrofísicos - Mendes, Raissa Fernandes Pessoa [UNESP] (2014)
Besides serving as eﬀective models for more complex interactions, scalar ﬁelds also arise as interesting extensions of General Relativity, candidates for dark matter or key ingredients in cosmological models. Their phenomenology is rich and may, in principle, be tested by experiments and observations. In particular, generalrelativistic stable spacetimes can be made unstable under the presence of certain nonminimally coupled free scalar ﬁelds. It has been shown that this instability may express itself quantum-mechanically through the ampliﬁcation of quantum ﬂuctuations and of the vacuum energy density of those ﬁelds. This eﬀect of vacuum dominance induced by gravity illustrates the important role that quantum eﬀects in curved spacetimes may have. The work presented in this Thesis aims at contributing to a deeper understanding of this eﬀect, along two main lines. First, we clarify the relationship between the quantum approach to instability and the classical analysis of quasinormal modes. In particular, we show how quantum ﬂuctuations can be simulated by classical perturbations of a certain amplitude. Second, we study the stability of nonminimally coupled ﬁelds in the spacetime of spheroidal and rotating thin shells of matter, in order to characterize how the parameter space of the instability changes when we drop previously assumed assumptions such as staticity and spherical symmetry of the background spacetime. The consideration of these aspects is mainly motivated by the possibility of using observational data of relativistic stars to constrain the ﬁeld couplings present in Nature. Possible observational implications of the instability and its relation to other results in the literature are also discussed