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Corrections and Additional Remarks to the Paper УKovariante Superpotentiale in der Allgemeinen RelativittstheorieФ.

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Annalen der Physik. 7. FoIge, Bond 32, Heft 6, 1976,s. 361-362
J. A. Barth, Leipzig
Corrections and Additional Remarks to the Paper
"Kovariante Superpotentiale in der AIIgemeinen Relativit&s-
theorid'
Von U. KASPER
Zentralinatitut fur Astrophysik der Akademie der Wieeenschaften der DDR, Potsdam-Babelaberg
In our paper') [l] we have given the covariant formulation of v. FREUD'S
superpotential. The starting point for that formulation was the use of tetrads which are
not neceseerily orthonorinalized and the demand that the tetrads and the basic vectors ofa certain holonomic coordinate system are identical.
If we start from the ansatz (1.39) for the tetrad field:
hAt
8~~
(1)
(which meens that the tetrads and the baaic vectors of a certain holonomic coordinate
system are identical), then the relation (1.41):
hAb;,
2 I..,, h A m
(2)
is obtained which is equivalent to
em
A hA,hrb,,.
(3)
Using expression (3), we get from the components
-I
of V. FREUD'S
superpotential the covariant formulation (1.35).
The argumentation which begins after eq. (1.44) and ends with eq. (1.48) is wrong
and has to be replaced by the following one. Correcting the relations (1.14) and (1.16)
we have the identities
and
and obtain, taking into consideration eqs. (1)and (2), the relation
a8
as
ws
+hA'.m
1)
aaAB,n.
aAB,m
. a8
=-
a!P,?Ig*,m
In later references thia papem will be quoted as I.
362
U.KASPER
where 2 is EINSTEIN'S
LAcRANoian density. Furthermore, the equation
holde, so that the well-known relations of EINSTEIN'S
theory follow froin eqs. (5)
and (6).
Relerenees
[l] U. KASPER,Ann. Physik 80, 147 (1973).
Bei der Redaktion eingegangen am 29. November 1974.
Anschr. d. Verf.: Dr. U. KASPEB
Zentralinst. f. Astrophysik d. AdW der DDR
DDR-1602 Potadam-Babelaberg, Rose-Luxemburg-Str. 178
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relativittstheorieф, paper, superpotentiale, уkovariante, remarks, corrections, der, additional, allgemeines
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