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arXiv:gr-qc/0406090v229Sep2005 REINSTATING SCHWARZSCHILD'S ORIGINAL
 

Summary: arXiv:gr-qc/0406090v229Sep2005
REINSTATING SCHWARZSCHILD'S ORIGINAL
MANIFOLD AND ITS SINGULARITY
SALVATORE ANTOCI AND DIERCK-EKKEHARD LIEBSCHER
Abstract. A review of results about this paradigmatic solution1
to the field
equations of Einstein's theory of general relativity is proposed. Firstly, an intro-
ductory note of historical character explains the difference between the original
Schwarzschild's solution and the "Schwarzschild solution" of all the books and the
research papers, that is due essentially to Hilbert, as well as the origin of the mis-
nomer.
The viability of Hilbert's solution as a model for the spherically symmetric field of
a "Massenpunkt" is then scrutinised. It is proved that Hilbert's solution contains
two main defects. In a fundamental paper written in 1950, J.L. Synge set two
postulates that the geodesic paths of a given metric must satisfy in order to comply
with our basic ideas on time, namely the postulate of order and the non-circuital
postulate. It is shown that neither Hilbert's solution, nor the equivalent metrics that
can be obtained from the latter with a coordinate tranformation that is regular and
one-to-one everywhere except on the Schwarzschild surface can obey both Synge's
postulates. Therefore they do not possess a consistent arrow of time, and the

  

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

 

Collections: Physics