Ted Jacobson 2007 Class. Quantum Grav. 24 5717 doi:10.1088/0264-9381/24/22/N02
Ted Jacobson
Show affiliationsThe Schwarzschild metric, its Reissner–Nordstrom–de Sitter generalizations to higher dimensions and some further generalizations all share the feature that gttgrr = −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.
53A45 Vector and tensor analysis
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
15A72 Vector and tensor algebra, theory of invariants (See also 13A50, 14L24)
Issue 22 (21 November 2007)
Received 1 August 2007, in final form 28 September 2007
Published 6 November 2007
Ted Jacobson 2007 Class. Quantum Grav. 24 5717
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