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

TL;DR

This paper develops tensorial, spinorial, and helicity formalisms for curvature dynamics in linearized gravity, providing new equations and demonstrating equivalences between different gravitational energy and momentum formulas.

Contribution

It introduces new formalisms for curvature dynamics in linearized gravity and proves the equivalence of key energy and momentum formulas within these frameworks.

Findings

Equivalence of Bia extl{}ynicki-Birula and Landau-Lifschitz energy formulas.

New equations for curvature dynamics in linearized gravity.

Analysis of gravitational radiation using curvature formalisms.

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 Bia\l{}ynicki-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.