برگزار شده توسط : دانشگاه حکیم سبزواری
سومين کنفرانس سيستم های ديناميکی و نظريه های هندسی
تاریخ برگزاری : 07 بهمن ماه 1400
Geometric Analysis of the Lie Algebra of Killing Vector Fields for a Significant Cosmological Model of Rotating Fluids
فاطمه آهنگری
The investigation of rotating fluids in the context of general relativity received remarkable consideration principally after Godel proposed relativistic model of a rotating dust universe. In this paper, a comprehensive analysis regarding the structure of the Lie algebra of Killing vector fields for a specific solution of field equations describing the behaviour of rotating fluid models is presented. Killing vector fields can be undoubtedly reckoned as one of the most substantial types of symmetries and are denoted by the smooth vector fields which preserve the metric tensor. Additionally, the flow corresponding to a Killing vector field generates a symmetry in a way that if each point moves on an object at the same distance in the direction of the Killing vector field then distances on the object will not distorted at all. Therefore, Killing vector fields are inherently expected to be of significant application in the study of geodesic motion. When one investigates the Lagrangian explaining the motion of a particle, one can realize that Killing vectors are the symmetries of the system and lead to conserved canonical momenta analogous to cyclic coordinates in classical mechanics. Taking into account the outstanding properties declared above, in this paper, we specifically concentrate on detailed investigation of the Killing vector fields by reexpressing the analyzed cosmological solution in the orthogonal frame. Significantly, for the resulted Lie algebra of Killing vector fields, the associated basis for the original Lie algebra is determined in which the Lie algebra will be appropriately decomposed into an internal direct sum of subalgebras, where each summand is indecomposable.
Killing vector fields, five dimensional spacetime, rotating fluids
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, 1400 , Geometric Analysis of the Lie Algebra of Killing Vector Fields for a Significant Cosmological Model of Rotating Fluids , سومين کنفرانس سيستم های ديناميکی و نظريه های هندسی
تاریخ برگزاری : 07 بهمن ماه 1400