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An addendum to Birkhoff’s theorem. (English) Zbl 0895.53059

Gen. Relativ. Gravitation 29, No. 4, 515-517 (1997); erratum ibid. 31, No. 6, 973 (1999).
Summary: In spherically symmetric systems, in spite of Birkhoff’s Theorem, the rates of clocks in vacuum regions on either side of moving mass shells must be continually readjusted to stay in synchrony. This shows up as time-dependence of the metric in terms of the globally meaningful time coordinate.

MSC:

53Z05 Applications of differential geometry to physics
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
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References:

[1] Hawking, S. W., and Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge). · Zbl 0265.53054
[2] Rindler, W. (1977). Essential Relativity (2nd ed., Springer-Verlag, New York/Heidelberg/Berlin). · Zbl 1063.83500
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