《Physical Interpretation of Vacuum Solutions of Einstein#39;s Equations I》.pdf

General Relar and Gravitation, Vol. 24, No. 5, 1992 Physical Interpretation of Vacuum Solutions of Einsteins Equations. Part I. Time-independent Solutions W . B. Boomer 1 Received 17 December 1991 This article is a review of interpretations which have been given to some well known solutions of the vacuum equations. Special attention is paid to those of Schwarzschild, Curzon and Kerr, and it is argued that the bizarre topologies they have been endowed with are physically unrealistic. Among others discussed are the two-centres solution of Bach and Weyl, the NUT solution, and solutions for an infinite line-mass, both static and rotating. 1. I N T R O D U C T I O N Relativists have not been diligent in interpreting solution of Einsteins equations. T h u s in the book of exact solutions [1] one finds m a n y whose physical m e a n i n g is unknown, or only p a r t i a l l y understood. One reason for this m a y be t h a t i n t e r p r e t a t i o n is difficult and uncer- tain. A n o t h e r reason is the following. T h e observational verification of general relativity, now and in the near future, is likely to d e p e n d on a very small n u m b e r of exact solutions: those of Schwarzschild and possibly Kerr, cosmological models, and p e r h a p s some g rav i tati o n al wave metrics. Some workers feel it is a waste of time to t r y to interpret metrics which have no p r o s p e c t of observational verification. Yet it seems to me t h a t we cannot claim to u n d e r s t a n d general rela- tivity unless we can d e t e r m