Time (in)dependence in general relativity
arXiv:gr-qc/0607020 · doi:10.1119/1.2426351
Abstract
We clarify the conditions for Birkhoff's theorem, that is, time-independence in general relativity. We work primarily at the linearized level where guidance from electrodynamics is particularly useful. As a bonus, we also derive the equivalence principle. The basic time-independent solutions due to Schwarzschild and Kerr provide concrete illustrations of the theorem. Only familiarity with Maxwell's equations and tensor analysis is required.
Revised version of originally titled "Kinder Kerr", to appear in American Journal of Physics