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arXiv:physics/0310104v121Oct2003 DAVID HILBERT AND THE ORIGIN OF THE
 

Summary: arXiv:physics/0310104v121Oct2003
DAVID HILBERT AND THE ORIGIN OF THE
"SCHWARZSCHILD SOLUTION"
SALVATORE ANTOCI
Abstract. The very early dismissal of Schwarzschild's original solution
and manifold, and the rise, under Schwarzschild's name, of the inequiva-
lent 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, in-
trinsic 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.
1. Introduction
There is, indisputably, no issue in Einstein's theory of general relativ-
ity that has been so accurately scrutinized, and by so many relativists in
so many decades, like the "Schwarzschild solution". Innumerable research
articles have been devoted to its study, and still are at the present day.

  

Source: Antoci, Salvatore - Dipartimento di Fisica, Universita' di Pavia

 

Collections: Physics