Curvature dynamics in General Relativity
arXiv:2211.10123 · doi:10.3390/universe9020110
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.
13 pages plus tittle page and abstract; revised version [v2]: small changes in text, acknowledgement and references added; [v3]: equation (22) simplified, appendix added