Einstein Equations and Hilbert Action: What is Missing on Page 8 of the Proofs for Hilbert's First Communication on the Foundations of Physics?1
In contrast to Einstein's discovery of special relativity in 1905, his path towards the theory of general relativity is documented by a rich historical record. Not only did Einstein publish quite a few papers on earlier versions of a generalized theory of rela tivity, we also have a number of research manuscripts from crucial periods of his search, and we have an extensive correspondence from the relevant years. Hilbert's involvement in the discovery of general relativity is less abundantly documented but also here we have a few key documents that shed light on his work. Compared to other episodes in the history of science, the history of general relativity is very well written, and specifically the competition between Einstein and Hilbert in the final weeks before the publication of generally covariant field equations of gravitation in late 1915 has been commented on extensively.2 Nevertheless, much of the historical literature on the Einstein-Hilbert competition took sides in what was perceived as a priority debate and it still seems worthwhile to come to a succinct and balanced assessment of the respective contributions of both authors in the final establishment of the general theory of relativity. In this respect, a set of proofs of Hilbert's relevant paper are of some significance and with those proofs the fact that a piece of them is missing. Although the fact that a piece of those proofs is missing is well known and was briefly commented on by several authors, the question naturally arises as to whether that missing part could have contained information that would compel us to reassess the historical account?
KeywordsRicci Tensor Einstein Tensor Variational Derivative Energy Concept HILBERT Action
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