Stationary field equations in the presence of a charged perfect fluid with both electric and monopole currents in isometric motion are studied. It is shown that the eight‐parameter group of transformations which preserve the stationary electrovac equations can also be applied to dually charged sources. In the case of dually charged dust an equilibrium condition ρ= (σ*σ)1/2 implies a functional relationship between ReΓ and the complex potentials Φ and Φ*. Furthermore, it is proved that when ρ≠0 and σ≠0, the additional assumption of an arbitrary linear relationship between Γ and Φ leads uniquely to the Israel–Spanos class of solutions.
REFERENCES
1.
2.
D.
Kramer
, G.
Neugebauer
, and H.
Stephani
, Forschr. Physik
20
, Heft 1, 1
(1972
).3.
For the historical development of these symmetries, see, e.g.,
H. A.
Buchdahl
, Quart. J. Math., Oxford Ser.
5
, 116
(1954
),and
S.
Kloster
, M. M.
Som
, and A.
Das
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15
, 1096
(1974
).4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Equations (2.1) reduce to (C.28) and (C.29) of KNS by letting and Note that KNS use signature which changes the signs of the last three terms of We define the dual of a tensor so that as in KNS, while some authors use the opposite sign.
14.
Cf. KNS Eq. (C.11). They use ψ for A and χ for Our
15.
See the derivation of Eq. (17) in IW.
16.
17.
These equations reduce to (C.42) of KNS. In their equations (b) and (c), the right sides should be and
18.
Table 7 of KNS. See also Kinnersley, Ref. 3.
19.
Some of these were applied to sources by
D.
Kramer
and G.
Neugebauer
, Ann. Physik
7
, Bd. 27, 129
(1971
).20.
This is a generalization of a transformation given by Buchdahl in Ref. 3.
21.
R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1966), Vol. II.
22.
Cf. sec 4 of IW.
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© 1977 American Institute of Physics.
1977
American Institute of Physics
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