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Published in last 50 years
Noether's theorem is applied to Hilbert's Lagrangian written as a functional of spinorial variables. The associatedSL(2,C) conserved current is obtained, and its expression for the Tolman metric is given explicitly.
An attempt is made to obtain a conformally invariant gravitational wave equation in an isotropic background universe by modifying the Einstein field equation through a correction term proposed in the Hilbert Lagrangian in the form of a series of finite terms inR (≡g ik R ik ). It is shown that only those waves which are described by Bessel functionJ 0(mη) in curved background can be transformed as classically periodic waves in flat background [without restricting the scale factora(η)].