The Hassan–Rosen bimetric theory is an extension of general relativity which considers the interaction between two metric fields defined on the same differentiable manifold. Self-accelerating cosmologies are exact solutions of this theory, and this makes it interesting to explore. We analyze the theory and see if it can provide other physically consistent solutions.

Despite the effort put in studying the theory in recent years, very few exact solutions are known in the literature, and the majority are equivalent to those of general relativity. A valuable approach to try to simplify the field equations and find exact solutions is to impose some spacetime symmetry on the system, e.g., spherical symmetry.

Our study is concerned with symmetries of spacetimes in Hassan–Rosen bimetric theory. Two metrics being present, we investigate what relations exist between their spacetime symmetries. We focus on the isometries of the metrics and clarify when they are the same.

We apply the results in exploring solutions in the Hassan–Rosen theory. We consider maximally symmetric solutions and black hole solutions, and find a previously unknown class of non-stationary spherically symmetric solutions. The existence of the class of non-stationary spherically symmetric solutions disproof a similar statement to Birkhoff's theorem in the Hassan–Rosen bimetric theory. The study of bidiagonal non-rotating black holes sharing the isometries focuses on their properties both at the shared Killing horizon and far from it.

The thesis is a review of these results, and the relevant papers accompany it.