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Birkhoff’s theorem with \(\Lambda\)-term and Bertotti-Kasner space. (English) Zbl 0959.83008

If a \(\Lambda\)-term is included, the usual generalization of Schwarzschild space is not the only possible spherically symmetric vacuum solution. Another is Bertotti-Kasner space, as has been noted before but not explicitly demonstrated. The purpose of this note is to reformulate the unicity theorem and to discuss the extra solution. Historically, the solution called Bertotti-Kasner space by the author, was already deduced in 1950 by H. Nariai [On some static solutions of Einstein’s gravitational field equations in a spherically symmetric case, Sci. Rep. Tôhoku Univ., Ser. I 34, 160-167 (1950) which has been reprinted in Gen. Relativ. Gravitation 31, 951-961 (1999)] together with a new introduction by A. Krasinski (see Zbl 0959.83009 below).

MSC:

83C15 Exact solutions to problems in general relativity and gravitational theory
83-03 History of relativity and gravitational theory
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory

Citations:

Zbl 0959.83009
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References:

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