Abstract. The Schwarzschild metric, its Reissner–Nordstrom–de Sitter generalizations to higher dimensions and some further generalizations all share the feature that g_ttg_rr = −1 in Schwarzschild-like coordinates. In this pedagogical note we trace this feature to the condition that the Ricci tensor (and stress–energy tensor in a solution to Einstein's equation) has vanishing radial null–null component, i.e., is proportional to the metric in the t–r subspace. We also show that this condition holds if and only if the area–radius coordinate is an affine parameter on the radial null geodesics.

PACS numbers: 04.20.Jb, 04.20.−q

Print publication: Issue 22 (21 November 2007)
Received 1 August 2007, in final form 28 September 2007
Published 6 November 2007