General Relativity: An Introduction for Physicists · Problem 14.15

The Friedmann–Robertson–Walker geometry — Hobson, Efstathiou & Lasenby

Physics · relativistic-continuity-equation-cosmological-fluid

Problem

Show that the relativistic equation of motion for the cosmological fluid is satisfied identically and that the relativistic equation of continuity takes the form ρ˙+(ρ+pc2)3R˙R=0.\dot{\rho} + \left(\rho + \frac{p}{c^2}\right)\frac{3\dot{R}}{R} = 0. Show further that this equation may also be written in the forms d(ρR3)dt=−3pR˙R2c2andd(ρR3)dR=−3pR2c2.\frac{d(\rho R^3)}{dt} = -\frac{3p\dot{R}R^2}{c^2} \qquad \text{and} \qquad \frac{d(\rho R^3)}{dR} = -\frac{3pR^2}{c^2}.

Related theory

Browse the problem library