General Relativity: An Introduction for Physicists · Problem 15.16

Cosmological models — Hobson, Efstathiou & Lasenby

Physics · k-minus-one-vacuum-friedmann-minkowski

Problem

For a k=−1k = -1 Friedmann model containing no matter or radiation, show that the line element becomes ds2=c2 dt2−c2t2[dχ2+sinh⁡2χ (dθ2+sin⁡2θ dϕ2)].ds^2 = c^2\,dt^2 - c^2t^2\left[d\chi^2 + \sinh^2\chi\,(d\theta^2 + \sin^2\theta\, d\phi^2)\right]. Show that this metric describes a Minkowski spacetime.

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