When is g(tt) g(rr) = -1?
Jul, 2007Citations per year
Abstract: (arXiv)
The Schwarzschild metric, its Reissner-Nordstrom-de Sitter generalizations to higher dimensions, and some further generalizations all share the feature that g_{tt} g_{rr} = -1 in Schwarzschild-like coordinates. In this pedagogical note we trace this feature to the vanishing of the radial null-null component of the Ricci tensor or, for solutions to Einstein's equation, the stress-energy tensor. We also show this condition holds if and only if the area-radius coordinate is an affine parameter on the radial null geodesics.- 04.20.-q
- 04.20.Jb
- Einstein equation
- space-time: Reissner-Nordstroem
- space-time: de Sitter
- space-time: Schwarzschild
- tensor: energy-momentum
- tensor: Ricci
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