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The Schwarzschild metric, its Reissner-Nordstrom-de Sitter generalizations tohigher dimensions, and some further generalizations all share the feature thatg_{tt} g_{rr}=-1 in Schwarzschild-like coordinates. In this pedagogical note wetrace this feature to the condition that the Ricci tensor (and stress-energytensor in a solution to Einstein's equation) has vanishing radial null-nullcomponent, i.e. is proportional to the metric in the t-r subspace. We also showthis condition holds if and only if the area-radius coordinate is an affineparameter on the radial null geodesics.

When is g_{tt} g_{rr} = -1?