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On the Nonexistence of a Class of Static Einstein Spaces Asymptotic at Infinity to a Space of Constant Curvature
1.R. Serini, Atti Accad. Nazl. Lincei (5) 27, 235 (1918). [Presented in outline in footnote reference 3.]
2.A. Einstein, Rev. Univ. Nac. Tucumán Ser. A, 2, 11 (1941).
3.A. Einstein and W. Pauli, Ann. Math. 44, 131 (1943).
4.A. Lichnerowicz, Compt. rend. 222, 432 (1946).
5.A. Lichnerowicz, Théories relativistes de la gravitation et de l’électromagnétisme (Masson, Paris, 1955), Chap. 8.
6.As regards roman indices, those denoted by the first eight letters of the alphabet run from 1 to 3, and the remaining letters from 1 to 4; is the timelike coordinate.
7.“Constant curvature” is always intended to mean constant Riemannian curvature.
8.The spinor analysis involved herein, and the notation used is that of L. Infeld and B. L. van der Waerden, Sitzber. preuss. Akad. Wiss. Physik. math. Kl. (1933), 380.
9.R. Bach, Math. Z. 9, 110 (1921).
10.C. Lanczos, Ann. Math. 39, 842 (1938).
11.Now and hereafter the signature of is always understood to be
12.Harish‐Chandra, Proc. Indian Acad. Sci. 23, 152 (1946).
13.L. P. Eisenhart, Riemannian Geometry (Princeton University Press, Princeton, New Jersey, 1926), Chap. II, p. 91.
14.See the argument of Sec. 5.
15.Footnote reference 13, Chap. 2, p. 85.
16.For the purposes of later sections weaker conditions upon the asymptotic behavior of and and of all the first derivatives of other than would actually be adequate.
17.One should then, to be consistent, restrict m to be non‐negative.
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