1 8 8 D O C . 2 0 R E L AT I V I T Y L E C T U R E N O T E S
Erweiterung der Feldgleichungen statt als Tensor
Erlaubte Erweiterung. Divergenz verschw. auch, weil Divergenz von ver-
schw., wenn λ Konstante ist.
AD (Harvey Plotnick, Chicago). [85 169]. The text appears on the recto and verso of an unnumbered
single sheet of paper.
This document is dated on the assumption that it is part of a set of notes made in preparation for
lectures at the University of Zurich in summer semester 1919. Such lectures are mentioned in the min-
utes of the meeting of 4 March 1919 of the Education Council of the Canton of Zurich (Auszug aus
dem Protokoll des Erziehungsrates des Kantons Zürich vom 4. März 1919). Einstein was in Zurich by
3 July 1919 (see Einstein to Pauline Einstein, 3 July 1919, NNPM Heineman Collection). The topics
that are covered correspond to those—“Mercury” (“Merkur”), “cosmological problem” (“Kosmolo-
gisches Problem”)—listed for the final three lectures in a “Plan for the Zurich Lectures. Summer
1919” (“Plan für die Züricher Vorles. Sommer 1919”), written on a page following Einstein’s notes
for a course on general relativity at the University of Berlin earlier in 1919 (see Doc. 19, note 2).
Moreover, the relevant portion of the notes for the latter course (see Doc. 19, [p. 21], [p. 22], [p. 25])
is very similar to this document. For further discussion of the identification and dating of this docu-
ment, see Janssen and Schulmann 1998, written in response to Mehra 1998a, in which it is suggested
that this document consists of research notes of November 1915 (see also Mehra 1998b).
The expression below gives the general form of a static metric. The notation here and below is
essentially the notation used in Weyl 1918b, secs. 29–30 (see also Weyl 1921, secs. 29 and 31). To the
right of the vertical line, the Christoffel symbols for a metric field of this form are evaluated. The
Christoffel symbols vanish unless either one or two of its indices are equal to 4 (Weyl 1918b uses “0”
instead of “4”). In the latter case, and ( ).
These expressions for the components of the Ricci tensor for a static line element are equivalent
to the expressions given in Weyl 1918b, p. 193 (see also Doc. 19, [p. 22] and note 69). The expression
to the right of defines the operation Δf (in Weyl 1918b, p. 193, this operation is written as
The minus sign in the expression for the spatial components of the Christoffel symbols should
be a plus sign (see Weyl 1918b, p. 200; see also Doc. 19, [p. 24] and note 88). In Weyl 1918b (p. 193),
an asterisk rather than a prime is used to distinguish the Christoffel symbols constructed out of
from those constructed out of .
The line element below gives the Schwarzschild-Droste solution of Einstein’s gravitational field
The derivation of the expression for the perihelion advance of an orbit in the field of a point mass
follows Weyl 1918b, pp. 202–205 (see also Doc. 19, [p. 24] and note 90).
Rik λgik – Rik
Räumliches System liefert
--κργαβ - 0 = + +
-- - f2ñρ á =
Ραβ κρ γαβ + 0 =
λ ist best. durch Gleichgew. Dichte.
Wird durch euklidische Welt nicht gelöst, wohl aber
, wobei R Krümmungs-
----- - =
- –--gαβ---------- = k′, α 1 2 3 , , =
R44 Δ2 f).