2003/10/21 by Salvatore Antoci
Physics and Astronomy · #physics.hist-ph #gr-qc
published as in "Meteorological and Geophysical Fluid Dynamics (a book to commemorate the centenary of the birth of Hans Ertel)", W. Schröder Editor, Science Edition, Bremen, 2004 · LaTeX, 12 pages
arxiv created 2003/10/21 · arxiv updated 2009/12/01
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.