Seminarium Teorii Względności i Grawitacji

The class of tensor fields on a smooth manifold that can serve as a spacetime geometry is severely restricted --- namely if the geometry is required to be able to carry matter field equations that are both predictive and quantizable.So restricted in fact, that even the spacetime dynamics are completely determined by the structure of any matter field equations the tensorial geometry is required to carry.The key result is that the construction of any gravitational dynamics (including but also beyond Einstein) is reduced from a vague physical question to a clear-cut mathematical task --- namely to the mere solution of a system of linear homogeneous PDEs.These results are therefore of immediate relevance to any study of modified spacetime kinematics and gravitational dynamics, and will be explained for a general audience of relativists in this talk.