In his milestone paper on general relativity, Einstein not only introduces the Einstein summation convention, but also (formula (45) in [1]) abbreviates a minus at the Christoffel symbols away by introducing the Gamma notation for the connection coefficients of his variant of the covariant derivative, constructed on cotangent space first from given geodesics.


In later standard literature the minus is gone. (E.g. Schrödinger p.66 [3])


Why, and who dropped it?




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Addendum/scholium:
Thanks for linking from a related question on
<https://hsm.stackexchange.com/questions/7974/notation-for-christoffel-symbols> !


The *physical relevance of that sign* might explain why it is gone, and I first thought about not asking on mathoverflow. But Einstein's introduction of the covariant derivative strikes me as masterful abstract differential geometry (of his time). Plus, it can be simplified and abstracted to general symmetric connections with given geodesics without Christoffel symbol stuff (if I'm not mistaken).
*I have not yet found it in other literature.*
(Already the standard geodesic equation with Christoffel symbols looks like an ugly case of superfluous zero to me. Like Einstein I prefer an own side for the 2nd derivative.)




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[1] A.Einstein: Die Grundlage der allgemeinen Relativitätstheorie (1916) p.802
<https://web.archive.org/web/20060830030952/http://www.alberteinstein.info/gallery/pdf/CP6Doc30_pp284-339.pdf>


[2] Manuscript of [1], translation and more:
H.Gutfreund, J.Renn: The Road to Relativity (2015) p.92 (German manuscript facsimile) p.209 (English translation).
<https://press.princeton.edu/books/hardcover/9780691162539/the-road-to-relativity>


[3] E.Schrödinger: Space-Time Structure (1950/4)
<https://www.cambridge.org/core/books/spacetime-structure/554B50728DF38139E42E60BBED654D85>



The Einstein minus convention, lost
Since the question has now narrowed down to "who lost the minus sign" in the Christoffel symbol, let me start a new thread: The OP asks for a reputable source, later than Einstein's 1916 paper, in which the minus sign is abandoned. I propose that it was Einstein himself who dropped it. Below I copy from his [1921 lectures](https://einsteinpapers.press.princeton.edu/vol7-doc/593) at Princeton University, page 46:


![](https://ilorentz.org/beenakker/MO/Einstein_1922.png)
