The Hassan-Rosen bimetric theory describes two interacting spin-2 fields, one massless and one massive. In this thesis, a complete canonical analysis of this theory is performed in the metric formulation and all constraints are computed. In particular, a secondary constraint, whose existence was in doubt, is shown to exist and evaluated explicitly, bringing the total number of constraints up to six. This, together with general covariance, is enough to eliminate the Boulware-Deser ghost and ensure that the theory propagates the appropriate seven degrees of freedom. The requirement that the constraints are preserved in time leads to a linear relation between the lapse functions of the two metrics. Knowing the explicit form of the ratio of the lapses is necessary for solving initial value problems. The ratio is computed for the special case where the metrics share the same spherical symmetry.

Since the bimetric theory is diffeomorphism invariant, it must contain four first class constraints whose Poisson brackets form a certain algebra. In general, it is possible to use this algebra to identify a metric. In this thesis, the four first class constraints of bimetric theory are identified and it is shown that their Poisson brackets indeed forms the algebra required by diffeomorphism invariance. However, the metric identified from the algebra turns out not to be unique, but to depend on a choice of variables. Additionally, it need not coincide with the gravitational metric.

The candidate nonlinear partially massless bimetric theory is also investigated in this thesis. It is shown that for this theory, the partially massless symmetry cannot be extended beyond cubic order in the action. This result is generalized to the most general two derivative theory of only two interacting spin-2 fields, showing that such a theory cannot possess the partially massless symmetry beyond cubic order.

General relativity (GR) is the standard physical theory describing gravitational interactions. All astrophysical and cosmological observations are compatible with its predictions, provided that unknown matter and energy components are included. These are called dark matter and dark energy.

In addition, GR describes the nonlinear self-interaction of a massless spin-2 field. In particle physics, there are both massless and massive fields having spin 0, 1 and 1/2. It is then well-justified to ask whether a mathematically consistent nonlinear theory describing a massive spin-2 field exists.

The Hassan–Rosen bimetric relativity (BR) is a mathematically consistent theory describing the nonlinear interaction between a massless and a massive spin-2 field. These fields are described by two metrics, out of which only one can be directly coupled to us and determines the geometry we probe.

Since it includes GR, BR is an extension of it and provides us with new astrophysical and cosmological solutions. These solutions, which may give hints about the nature of dark matter and dark energy, need to be tested against observations in order to support or falsify the theory. This requires predictions for realistic physical systems. One such system is the spherically symmetric gravitational collapse of a dust cloud, and its study is the overarching motivation behind the thesis.

Studying realistic physical systems in BR requires the solving of the nonlinear equations of motion of the theory. This can be done in two ways: (i) looking for methods that simplify the equations in order to solve them exactly, and (ii) solving the equations numerically.

The studies reviewed in the thesis provide results for both alternatives. In the first case, the results concern spacetime symmetries (e.g., spherical symmetry) and how they affect particular solutions in BR, especially those describing gravitational collapse. In the second case, inspired by the success of numerical relativity, the results initiate the field of numerical bimetric relativity. The simulations provide us with the first hints about how gravitational collapse works in BR.