(Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022) Aras, Ulaş.; Bleeken, Dieter Van den.
In this thesis, we will give a review of torsion-free Newton- Cartan theory. We will start by doing a large c expansion of general relativity and we will restrict ourselves to a few leading orders. After obtaining Newton-Cartan theory in this way, we will explore its symmetries. Through a special set of combined symmetries, we will construct a split space and time structure. Lastly, we will work out the field equations and equations of motion for a particle in the 3+1 formulation we have obtained.