Introduction to Jebsen's paper

Abstract

Brief comment on a 1921 paper by Jebsen.

This work provides the first published proof of “Birkhoff's” theorem. The author, who seems to have been an undergraduate at the time (tragically, he died shortly afterwards) understood (as did many others) that Einstein's equations reduced considerably in a “minimal,” namely two-component, metric in a simple gauge such as Schwarzschild's; a good part of the paper is devoted to deriving this interval form.

The originality of his work lies instead in showing that time-independence of the exterior Schwarzschild solution need not be assumed, but is a consequence of Einstein's equations.

From a modern perspective, it is a bit surprising that this result was not found earlier: for example, Einstein studied the spherical solution in the linearized theory, whose kinship to Maxwell's might have suggested the obvious parallel to charge conservation. In current language, the theorem states gauge theories forbid monopole radiation because they have no helicity zero modes.

Editor's note: Further references to early derivations of “Birkhoff's” theorem can be found in [1] and [2] while [3] is one of the few papers that calls it “Jebsen-Birkhoff.” Since few's was written a more detailed biography of Jebsen has now appeared: gr-qc/0508163, by Johausen & Ravulal. Work supported by NSF Grant PHY04-00609