Gravitational quasi-normal modes of charged spherically symmetric black holes surrounded by quintessence fluid in Rastall gravity

We apply the WKB approximation method, matrix method, and finite difference method to study the gravitational quasi-normal modes of charged spherically symmetric black holes surrounded by quintessence fluid in Rastall gravity. By comparing the spherically symmetric spacetime metric of charged black holes surrounded by quintessence fluid in Rastall gravity with that of general relativity, we can find that the modifications to general relativity in this modified gravity theory can be described by parameters such as λ, Q, and Ca, etc. In four-dimensional spacetime, we investigate the impact of charge Q and parameter Ca on the gravitational quasi-normal modes of charged black holes surrounded by quintessence field in Rastall gravity. The aim is to search for observational evidence of such black holes in astrophysical observations and,consequently, test the validity of Rastall theory. In five-dimensional（5D） spacetime, we study the impact of the parameter Ca on the gravitational quasi-normal modes of Rastall black holes surrounded by quintessence field and summarize the corresponding variation patterns.