2 8 D O C . 1 G R AV I TAT I O N A L WAV E S
gravitational energy-momentum should be replaced by a generally covariant one (Levi-Civita 1917b,
p. 382). For further discussion of this issue, see sec. 6.
[34]In this equation the factor 1/2 should be 1/4, because of the extra factor 1/2 found in eq. (22).
[35]Levi-Civita 1917a, 1917b, 1917c, 1917d, 1917e. On Levi-Civita’s contribution to general rela-
tivity, see, e.g., Goodstein 1983.
[36]Levi-Civita 1917b.
[37]See Einstein to Tullio Levi-Civita, 2 August 1917 (Vol. 8, Doc. 368), and Tullio Levi-Civita to
Einstein, 23 August 1917 (Vol. 8, Doc. 375). For a discussion of this exchange between Einstein and
Levi-Civita, see Cattani and De Maria 1993.
[38]“ should be .”
[39]Four years later, Arthur S. Eddington commented: “As Einstein has pointed out, the investiga-
tion of this paragraph [Eddington is referring to sec. 6 of his own paper] gives the total loss of energy
of the material system correctly, but the intermediate steps are merely analytical. The lost energy is
not localisable anywhere.” Eddington 1922, p. 280.
[40]Levi-Civita 1917b (see also the correspondence cited in note 37) and Lorentz 1916, sec. 52. See
Einstein 1918f (Doc. 9), note 5, for the names of other colleagues objecting to the use of a nongener-
ally covariant quantity to represent gravitational energy-momentum density, as well as Einstein’s own
footnote 1 on p. 448 of Einstein 1918f (Doc. 9).
[41]Note that is the negative of what is now called the Einstein tensor. Einstein had previously
written the field equations in terms of the Ricci tensor.
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