Aneta Wojnar

A vector field as an observer in curved spacetime

In Einstein's General Relativity a gravitational interaction is represented by a metric on (curved) spacetime manifold with the Lorentzian signature ((-,+,+,+)) which satisfies the Einstein's field equations. An observer is an independent notion and according to a nowadays point of view she can be identified with the arrow of time. More precisely, the observer is a normalized timelike vector field on spacetime. We can also think about she as a collection of integral curves of that field. Physically speaking, they are world lines of some material object. Following Ehlers, we treat the observer as a flow of a fluid. It turns out that a pair: the metric and the vector field determines a geometrical object on a spacetime manifold which is called an almost-product structure. Our work is an attempt to connect physical properties of an observer's motion against 36 classes of a pseudo-Riemannian manifold (Naveira's classification), equipped with the almost-product structure. Studing a projected relative velocity of two material points it turns out we can decompose an obtained tensor into irreducible parts which have physical interpretations. The last part of the seminar will show us that we have just 16 classes of observers in GR.