Seminarium Teorii Względności i Grawitacji

I want to present few results from my Master Thesis concerning equvalence between the three variational principles ("pictures") used in general relativity: the metric picture (the most popular one, where the metric tensor plays role of the the primary object), the Palatni picture (here both the metric tensor and the connection are treated as a priori independent objects) and the affine picture (the least known, where the spacetime connection is primary). Such construction shows quite interesting fact: the non-metricity of the connection arises as a natural consequence of the properties of the matter field. As an example I will present the model of gravity with cosmological constant and its natural generalization which unifies the gravity with electromagnetism. The model realizes few ideas which strongly influenced XX-century theoretical physics:1) Weyl's concept of a non-metric connection, where "non-metricity" is described by the electromagnetic field, 2) Einstein's idea of unification: gravity and electromagnetism should correspond to the symmetric and the antisymmeric part, respectively, of the same geometric object. In case of our model this unifying object is the Ricci tensor of a non-metric connection, 3) Born-Infeld generalisation of electrodynamics, where the standard, linear Maxwell theory arises as an approximation of a certain non-linear, but very natural from geometric point of view, theory. At the end I shortly describe some problems of the so called "Weyl conformal gravity theories" and an interesting perturbation of the Proca theory. Zoom: 814 7211 6408Passcode: 795365