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 review how the equivalence principle results from general relativity. 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.
REFERENCES
1.
R.
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, New York, 1962
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For the history and a modern derivation, see
S.
Deser
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Roy P.
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Robert H.
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Charles W.
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(to be published).7.
The transformation that takes us back to Cartesian coordinates in this case is: , , and .
© 2007 American Association of Physics Teachers.
2007
American Association of Physics Teachers
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