General Relativity: An Introduction for Physicists · Problem 11.1

Schwarzschild black holes — Hobson, Efstathiou & Lasenby

Physics · schwarzschild-coordinates

Problem

In the Schwarzschild geometry, we introduce the new coordinates x=rsin⁡θcos⁡ϕ,y=rsin⁡θsin⁡ϕ,z=rcos⁡θ.x = r\sin\theta\cos\phi, \qquad y = r\sin\theta\sin\phi, \qquad z = r\cos\theta. Find the form of the line element in these coordinates.

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