پديد آورنده :
خشت زر، ماندانا
عنوان :
هندسه ي نظريه ي نسبيت عام و نظريه ي اينشتين
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
[نه]، [122]ص.
استاد راهنما :
قهرمان طاهريان، بهروز ميرزا
توصيفگر ها :
خميدگي , پيچش , چارچوبه كلاف
استاد داور :
اعظم اعتماد، فريد بهرامي
تاريخ ورود اطلاعات :
1398/03/22
تاريخ ويرايش اطلاعات :
1398/03/27
چكيده انگليسي :
Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Sayed Ghahreman TaherianSupervisor Dr Behrouz Mirza2000 MSC 55R10 53C05 83C05 53C07 Keywords Curvature torsion general relativity frame bundle Abstract This thesis is based on a new review of general relativity appeared in a paper of Miguel Socolovsky cf 22 Inthis article Socolovsky presents in the most natural way that is in the context of the theory of vector and principalbundles and connections in them fundamental geometrical concepts related to general relativity GR and one of itsextensions the Einstein Cartan theory EC For this purpose we express at first the concepts of covariant derivation parallel transport geodesics metricscompatible with the connection Riemann Cartan with or without torsion of Levi Civita and the concepts of curva ture and torsion using their geometric interpretation of the theory of vector bundles and their connections especiallyusing bundles of a Riemannian or pseudo Riemannian manifold The Einstein tensor is shown to appear naturally from the Bianchi identities thus emphasizing the pure geomet rical nature of the left hand side of the equations of general relativity Central concepts are the curvature tensor R the torsion tensor T and the non metricity tensor Q D g as properties of connections in a Riemannian or pseudo Riemannian manifold with metric g and a ne connection D is the covariant derivative with respect to General relativity has to do with a metric symmetric connection the Levi Civita connection that only allows for R Einstein Cartan theory involves a metric but not necessarily symmetric connection that allows also forT while the theory of Weylian manifolds involves a non necessarily metric Q 0 and non necessarily symmetric T 0 connection In units of length L we have R L 2 T Q L 1 while g L 0 One of the most beautiful equations of Physics is the equality to zero of the Einstein tensor that is the Einstein sequations in vacuum G 0where 1 G R g R 2 R g R g g R g R Equation G 0 is equivalent to Ricci atness R 0
استاد راهنما :
قهرمان طاهريان، بهروز ميرزا
استاد داور :
اعظم اعتماد، فريد بهرامي
