Newton to Einstein - dust to dust

Understand

We investigate the relation between the standard Newtonian equations for a pressureless fluid (dust) and the Einstein equations in a double expansion in small scales and small metric perturbations.

• We find that parts of the Einstein equations can be rewritten as a closed system of two coupled differential equations for the scalar and transverse vector metric perturbations in Poisson gauge.
• It is then shown that this system is equivalent to the Newtonian system of continuity and Euler equations.
• Brustein and Riotto (2011) conjectured the equivalence of these systems in the special case where vector perturbations were neglected.