Lo pseudotensore energia-impulso in teorie estese della gravitazione

Abstract

The gravitational field’s energy and momentum definitions are treated in extensive gravitation theories, through the generalization of the energymomentum pseudotensor, defined by Einstein in general relativity. This extension was obtained by modifying the Lagrangian of Hilbert-Einstein or by using a different connection from the one of Levi- Civita as that of Weitzenböck for teleparallel theories. We have firstly obtained the gravitational energy-momentum pseudotensor for extended Lagrangians that depend on the metric gμ⌫ and on its derivatives up to nth order and then demonstrated, in general, its affine and non-covariant behavior. Then we applied the weak field limit to Euler-Lagrange equations associated to the Lagrangian which depends linearly on the ⇤R terms and derived the modified gravitational waves with six polarization states, three transverse and three not, with helicity 0 and 2. Subsequently we have obtained, through the Noether theorem for infinitesimal rigid translations, the relative energy-momentum pseudotensor and after having developed it to the order h2 and mediated on an suitable domain, we have calculated the power emitted from a possible gravitational radiant source. For gravity f (R) and f (T) we have obtained the respective energy-momentum pseudotensors and, via the border therm B which connects the curvature R to the torsion T, we have studied the relative pseudotensor ⌧↵ #|!(T,B) allowing us to link ⌧↵ #|f(R) and ⌧↵ #|f(T). Finallywehave obtained the equations for two theories of higher order telepallel gravity: in particular for the Lagrangian L⇤kT = h ! T + Pp k=0 akT⇤kT # and for the sixth order telepallel gravity equivalent to LR⇤R = p−g (−R + a0R2 + a1R⇤R). [edited by author]