Abstract
The most general time-independent spherically symmetric (in the usual three space dimensions) solution to the five-dimensional vacuum Einstein equations is found, subject to the existence of a Killing vector in the fifth direction. The significance of these solutions is discussed within the context of a previously proposed extension of the Kaluza-Klein model in which the universe, although (4+1)-dimensional, has evolved over cosmic times into an effectively (3+l)-dimensional one.
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Chodos, A., Detweiler, S. Spherically symmetric solutions in five-dimensional general relativity. Gen Relat Gravit 14, 879–890 (1982). https://doi.org/10.1007/BF00756803
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DOI: https://doi.org/10.1007/BF00756803