Some consequences of nonstandard Lagrangians with time-dependent coefficients in general relativity

Nonstandard Lagrangians entitled ‘nonnaturals’ by Arnold have recently gained increasing importance bothin applied mathematics and in physical theories. These types of Lagrangians appear in some group ofdissipative dynamical systems, and they play an important role in a number of field theories. However, therole of nonstandard Lagrangians in geometric theories like general relativity is still absent. In thiscommunication, we would like to discuss the relevance of nonstandard Lagrangians in general relativityusing the principles of calculus of variations. In fact, nonstandard Lagrangians came in different forms,features, and characteristics, depending on the nature of the dynamical problem under study. In this work,we will be concerned with time-dependent Lagrangians of the form L1 + γ(t). After deriving the modifiedgeodesic equation using the basic techniques of Riemannian differential geometry which will be used toaxiomatize a large part of our work, we show that many interesting consequences will be raised accordinglywhen applied to FRW cosmology.

کلیدواژه ها:

Nonstandard Lagrangian ، Modified geodesic equation ، FRW cosmology