When is g(tt) g(rr) = -1?

Jul, 2007
3 pages
Published in:
  • Class.Quant.Grav. 24 (2007) 5717-5719
e-Print:

Citations per year

2007201220172022202502468101214
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