Curvature dynamics in General Relativity

TL;DR

This paper reformulates Einstein's equations as a wave equation for the Weyl tensor, establishing a curvature wave perspective, proving polarization states, and rederiving the quadrupole formula within a new theoretical framework.

Contribution

It introduces a novel formulation of General Relativity using curvature waves, providing new insights into gravitational wave polarization and extending linear results to non-linear regimes.

Findings

Existence of two transverse polarization states for curvature waves

Re-derivation of the quadrupole formula in the linearized approximation

Outline of a perturbative scheme for non-linear extensions

Abstract

The equations of General Relativity are recast in the form of a wave equation for the Weyl tensor. This allows to reformulate gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse polarization states for curvature waves is proven and in the linearized approximation the quadrupole formula is rederived. A perturbative scheme to extend the linearized result to the non-linear regime is outlined.