Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

An unambiguous definition of gravitational energy remains one the unresolved issues physics today. This problem is related to non-localization density. In General Relativity, there have been many proposals for defining density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, Møller, Weinberg. this review, we firstly explored energy–momentum complex in an nth order Lagrangian L=Lgμν,gμν,i1,gμν,i1i2,gμν,i1i2i3,⋯,gμν,i1i2i3⋯in then a as Lg=(R¯+a0R2+∑k=1pakR□kR)−g. Its part was obtained invariance action under infinitesimal rigid translations using Noether’s theorem. We also showed that tensor, general, not covariant object but only affine object, is, pseudo-tensor. Therefore, pseudo-tensor ταη becomes introduced Einstein if limit ourselves Relativity its extended corrections explicitly indicated. The same method used derive fR gravity both Palatini metric approaches. Moreover, weak field approximation lowest perturbation h calculated. As practical application, power per unit solid angle Ω emitted localized source carried wave direction x^ fixed number k suitable gauge obtained, through average value over spacetime domain local conservation cosmological flat Friedmann–Lemaître–Robertson–Walker spacetime, matter density f(R) formalism proposed. could be useful tool investigate further modes radiation beyond two standard required deal with non-local theories involving □−k terms.