The Szekeres inhomogeneous cosmological models are invariantly characterized as a subclass of the algebraically special type {22} solutions of the Einstein field equations for irrotational dust, and their relationship to the locally rotationally symmetric dust solutions is clarified.

1.
P.
Szekeres
,
Commun. Math. Phys.
41
,
55
(
1975
). We point out a number of minor errors in the form of the solutions given on page 61: In class (i), u(r) and w(r) should satisfy u(r)+w(r) = 0; in class (ii), u(r) and w(r) should satisfy u(r)−w(r) = 0; in class (iiia), the density should be κρ = (4/3)σ/t4/3(μ+φσ).
The existence of these errors has also been pointed out by
W. B.
Bonnor
and
N.
Tomimura
,
Mon. Not. R. Astron. Soc.
175
,
85
(
1976
). The coordinates used in this paper are analogous to the coordinates used in Ref. 3.
2.
This class of solutions is characterized by the fact that they admit a (local) group of isometries which acts multiply transitively on the group orbits.
3.
G. F. R.
Ellis
,
J. Math. Phys.
8
,
1171
(
1967
).
4.
E. T.
Newman
and
R.
Penrose
,
J. Math. Phys.
3
,
566
(
1962
).
For more details and a complete listing of the Newman—Penrose equations see F. A. E. Pirani, in Brandeis Summer Institute in Theoretical Physics Lectures on General Relativity (Prentice‐Hall, Englewood Cliffs, N.J., 1964).
5.
J. M.
Stewart
and
G. F. R.
Ellis
,
J. Math. Phys.
9
,
1072
(
1968
).
6.
J.
Wainwright
,
Commun. Math. Phys.
17
,
42
(
1970
).
7.
H. Cartan, Differential Forms (Kershaw, London, 1971), 97. Note that Eq’.s (2.7 reads dk∧k∧n = 0dn∧n∧k in differential form notation.
8.
Szekeres pointed out that his solutions contain the Tolman—Bondi solutions [
H.
Bondi
,
Mon. Not. R. Astron. Soc.
410
,
107
(
1947
)],
the Kantowski—Sachs solutions [
R.
Kantowski
and
R. K.
Sachs
,
J. Math. Phys.
7
,
443
(
1966
)],
and a class of solutions discussed by
D.
Eardley
,
E.
Liang
, and
R. R.
Sachs
,
J. Math. Phys.
13
,
99
(
1972
), which are known to be LRS Class II solutions.
9.
The first of equations (3.4) is satisfied by all LRS perfect fluid solutions, the second only by Classes I and II.
10.
H.
Stephani
,
Commun. Math. Phys.
9
,
53
(
1968
).
11.
Not all type {22} solutions of the Einstein equations with a perfect fluid source satisfy Property (A). An example of one which does not is a solution given by
H.
Wahlquist
,
Phys. Rev.
172
,
1291
(
1968
).
12.
M. Olesen, “Algebraically Special Fluid Space—Times with Shearing Rays,” Ph.D. thesis, University of Waterloo, 1972 (unpublished).
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