On black holes surrounded by a fluid of strings in Rastall gravity

We obtain the exact solution of the field equations in the framework of the Rastall gravity for a static, charged and spherically symmetric black hole surrounded by a fluid of strings and analyze the behavior of the horizons, mass, Hawking temperature and geodesics in terms of the parameter related to the presence of the fluid as well as on the parameter beta of the Rastall gravity. We discuss some particular cases and the fact that a subclass of the obtained solutions can be mapped to black hole solutions obtained in the framework of general relativity. We also obtain a class of solutions which correspond to a rotating, charged black hole surrounded by a fluid of strings, by applying an algorithm to construct rotating solutions from the static solutions. The horizons, mass, Hawking temperature, ergoregions and geodesics are examined. The role played by the presence of the fluid of strings and the characteristics arising from the Rastall gravity are emphasized.