Curvature and conformal curvature dynamics formalisms and their applications in linearized gravity

Abstract

Tensorial, spinorial and helicity formalisms of the curvature and conformal curvature dynamics are developed. Equations of linearized gravity within that formalisms are given. Gravitational radiation in linearized gravity in terms of curvature dynamics is investigated. Equivalence of the Białynicki-Birula formula for the gravitational energy in linearized gravity and the Landau–Lifschitz formula is proved. Analogous result is found for the momentum in linearized gravity.