The tenuous interplanetary medium along the Earth-Moon line has a rest-frame mass density

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Einstein's field equations · Einstein's field equations

The Geometry of Gravity, Ch The Einstein field equations and the Newtonian limit

Problem

The tenuous interplanetary medium along the Earth-Moon line has a rest-frame mass density ρm=1.0×10−20 kg m−3\rho_{\rm m} = 1.0\times10^{-20}\,\mathrm{kg\,m^{-3}}, modelled as dust at rest in this frame, so that its trace is T=−ρmc2T = -\rho_{\rm m}c^2. Take Λ=0\Lambda=0 at this scale, and use κ=8πG/c4=2.08×10−43 s2 m−1 kg−1\kappa = 8\pi G/c^4 = 2.08\times10^{-43}\,\mathrm{s^2\,m^{-1}\,kg^{-1}}. ((a)) Write the field equations with Λ\Lambda and identify each symbol. ((b)) Using the trace of the field equations, R=−κTR=-\kappa T, compute the Ricci scalar RR at this location.

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