Abstract
A number of different forms of the Schwarzschild solution are considered. The static forms all have a singularity at the Schwarzschild radius. This Schwarzschild singularity can be eliminated if one goes over to a stationary or time-dependent form of solution. However, the coordinate transformations needed for this have singularities. It is stressed that coordinate systems connected by singular transformations are not equivalent and the corresponding metrics may describe different physical situations.
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References
N. Rosen, inRelativity, M. Carmeli, S. I. Fickler, and L. Witten, eds. (Plenum Press, New York, 1970), p. 229.
N. Rosen,Nuovo Cimento B 72, 51 (1982).
V. Fock, The Theory of Space, Time and Gravitation (Pergamon Press, Oxford, 1964), 2nd edn., p. 193.
L. Landau and E. Lifshitz,The Classical Theory of Fields (Pergamon Press, Oxford, 1975), 4th edn., p. 282.
N. Rosen,Found. Phys. (to appear).
A. S. Eddington,Nature (London) 113, 192 (1924).
D. Finkelstein,Phys. Rev. 110, 965 (1958).
M. D. Kruskal,Phys. Rev. 119, 1743 (1960).
G. Szekeres,Publ. Mat. Debrecen 7, 285 (1960).
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Rosen, N. Some Schwarzschild solutions and their singularities. Found Phys 15, 517–529 (1985). https://doi.org/10.1007/BF01889285
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DOI: https://doi.org/10.1007/BF01889285