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

Abstract

AbstractNonstandard Lagrangians entitled ânonnaturalsâ by Arnold have recently gained increasing importance both in applied mathematics and in physical theories. These types of Lagrangians appear in some group of dissipative dynamical systems, and they play an important role in a number of field theories. However, the role of nonstandard Lagrangians in geometric theories like general relativity is still absent. In this communication, we would like to discuss the relevance of nonstandard Lagrangians in general relativity using 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 modified geodesic equation using the basic techniques of Riemannian differential geometry which will be used to axiomatize a large part of our work, we show that many interesting consequences will be raised accordingly when applied to FRW cosmology.