# fluid mechanics in FLRW-models

17 May 2023Covariant energy-momentum conservation \(g^{\alpha\mu}\nabla_\alpha T_{\mu\nu}=0\) projected onto the world line of an FLRW-observer with \(u_\nu=(c,\vec{0})\) yields the continuity equation \(\dot{\rho}+3H(1+w)\rho=0\). Whatâ€™s the projection perpendicular to it?