Newton-Cartan gravity

Geometrical reformulations of non-relativistic gravity, such as Newton- Cartan, have seen a surge in popularity due to their applications in holography and condensed matter physics. In this thesis, we discuss the construction of Newton-Cartan gravity through a gauging procedure of the Bargmann algebra, which is the central extension of the Galilei algebra. In order to achieve this goal, we recall the vielbein formalism of general relativity and how a gauging of the Poincaré algebra results in its off shell formulation. The procedure is then generalized in the non-relativistic case and it yields the transformation rules for all fields and the corresponding curvatures.Geometrijskim reformulacijama nerelativističke gravitacije, poput Newton- Cartanove, narasla je popularnost zbog njihovih primjena u holografiji i fizici čvrstog stanja. Ovaj diplomski rad bavi se konstrukcijom Newton-Cartanove gravitacije baždarenjem Bargmannove algebre, koja je centralno proširena Galileieva algebra. Da bismo to postigli, prvo se prisjećamo vielbein formalizma opće teorije relativnosti te kako se baždarenjem Poincaréove algebre dobije navedena formulacije van ljuske. Ista procedura koristi se za nerelativistički slučaj te daje pravila transformacije svih baždarnih polja i pripadnih zakrivljenosti