Einstein Equations and Hilbert Action: What is missing on page 8 of the proofs for Hilbert's First Communication on the Foundations of Physics? |
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Authors: | Tilman Sauer |
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Institution: | (1) Einstein Papers Project, California Institute of Technology, 20-7 Pasadena, CA 91125, USA |
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Abstract: | The history of the publication of the gravitational field equations of general relativity in November 1915 by Einstein and
Hilbert is briefly reviewed. An analysis of the internal structure and logic of Hilbert's theory as expounded in extant proofs
and in the published version of his relevant paper is given with respect to the specific question what information would have
been found on a missing piece of Hilbert's proofs. The existing texts suggest that the missing piece contained the explicit
form of the Riemann curvature scalar in terms of the Ricci tensor as a specification of the axiomatically underdetermined
Lagrangian in Hilbert's action integral. An alternative reading that the missing piece of the proofs already may have contained
the Einstein tensor, i.e. an explicit calculation of the gravitational part of Hilbert's Lagrangian is argued to be highly
implausible. |
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Keywords: | |
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