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

We study the small speed of light expansion general relativity, utilizing modern perspective on non-Lorentzian geometry. This is an around ultra-local Carroll limit, in which cones close up. To this end, we first rewrite Einstein-Hilbert action pre-ultra-local variables, closely related to 3+1 decomposition relativity. At leading order expansion, these variables yield geometry and resulting des...

The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. equations motion and stress-energy-momentum tensor for hyperelastic body are derived the gauge-invariant action principle first considered by DeWitt. This natural extension single particle. central object in Lagrangian treatment Landau-Lifshitz radar metric, which version right Cauc...