TL;DR
This paper examines the Kruskal-Szekeres completion of Schwarzschild spacetime, addressing methodological criticisms by deriving KS coordinates from Israel coordinates and directly from Einstein equations.
Contribution
It introduces two new derivations of the KS coordinates, enhancing the understanding of their foundational construction.
Findings
KS coordinates can be derived from Israel coordinates
Direct derivation from Einstein equations is feasible
Addresses Synge's criticism of the KS procedure
Abstract
The Kruskal - Szekeres (KS) completion of the Schwarzschild spacetime is open to Synge's methodological criticism that the KS procedure generates "good" coordinates from "bad". This is addressed here in two ways: First I generate the KS coordinates from Israel coordinates, which are also "good", and then I generate the KS coordinates directly from a streamlined integration of the Einstein equations.
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