David Hilbert and the origin of the "Schwarzschild solution"

Details David Hilbert and the origin of the "Schwarzschild solution" David Hilbert and the origin of the "Schwarzschild solution"

2003-10-21

arxiv.org/abs/physics/0310104v1

in "Meteorological and Geophysical Fluid Dynamics (a book to commemorate the centenary of the birth of Hans Ertel)", W. Schr\"

Physics

History and Philosophy of Physics

LaTeX, 12 pages

Scientific paper

The very early dismissal of Schwarzschild's original solution and manifold, and the rise, under Schwarzschild's name, of the inequivalent solution and manifold found instead by Hilbert, are scrutinised and commented upon, in the light of the subsequent occurrences. It is reminded that Hilbert's manifold suffers from two defects, that are absent in Schwarzschild's manifold. It does not admit a consistent drawing of the arrow of time, and it allows for an invariant, local, intrinsic singularity in its interior. The former defect is remedied by the change of topology of the extensions proposed by Synge, Kruskal and Szekeres. The latter persists unaffected in the extensions, since it is of local character.

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