Buchdahl [Q. J. Math. 8, 89 (1957) and 9, 257 (1958)] has proposed the study of gauge-invariant generalization of field theories with asymmetric fundamental tensor. In this paper, the solution of plane gravitational waves in these Buchdahl's field theories have been investigated by the authors in plane symmetric space-time. Plane symmetry was studied and defined by Taub [Ann. Math. 53, 472 (1951)]. It has been shown that these solutions become identical with those of strong field equations of Einstein’s nonsymmetric unified field theory in plane symmetry under certain cases.

Topics
Energy system, Electromagnetism, Covariant formulation, General relativity, Gravitational waves, Multivariable calculus, Non Euclidean geometry, Riemannian geometry, Gauge field theory, Unified field theory
1.
Buchdahl
,
H. A.
, “
Gauge-invariant generalization of field theories with asymmetric fundamental tensor
,”
Q. J. Math.
https://doi.org/10.1093/qmath/8.1.89
 
8
,
89
(
1957
).
Google Scholar
Crossref
Search ADS
 
2.
Buchdahl
,
H. A.
, “
Gauge-invariant generalization of field theories with asymmetric fundamental tensor II
,”
Q. J. Math.
https://doi.org/10.1093/qmath/9.1.257
 
9
,
257
(
1958
).
Google Scholar
Crossref
Search ADS
 
3.
Weyl
,
H.
,
Raum-Zeit-Materie
, 3rd ed. (
Springer
,
Berlin
,
1919
).
Google Scholar
Crossref
Search ADS
 
4.
Einstein
,
A.
,
The Meaning of Relativity
, 5th ed. (
Princeton University Press
,
London
,
1955
), Appendix II.
Google Scholar
 
5.
Papapetrou
,
A.
, “
Static spherically symmetric solutions in the unified field theory
,”
Proc. R. Ir. Acad., Sect. A
 
52
,
69
(
1948
).
Google Scholar
 
6.
Lal
,
K. B.
 and
Shrivastava
,
R. P.
, “
On plane wave solutions of gauge-invariant generalization of field theories with asymmetric fundamental tensor in Bondi space-time
,”
Tensor
 
25
,
97
(
1972
).
Google Scholar
 
7.
Lal
,
K. B.
 and
Shrivastava
,
R. P.
, “
On the plane waves of gauge-invariant generalization of field theories with asymmetric fundamental tensor in a generalized Takeno space-time
,”
Tensor
 
27
,
7
(
1973
).
Google Scholar
 
8.
Taub
,
A. H.
, “
Empty space-times admitting a three parameter group of motions
,”
Ann. Math.
https://doi.org/10.2307/1969567
 
53
,
472
(
1951
).
Google Scholar
Crossref
Search ADS
 
9.
Takeno
,
H.
, “
The mathematical theory of plane gravitational waves in general relativity
,”
Sci. Rep. Res. Inst. Theor. Phys., Hiroshima University
, Vol.
1
(
1961
).
Google Scholar
 
10.
Hlavaty
,
V.
,
Geometry of Einstein’s Unified Field Theory
(
Noordhooff
,
Groningen
,
1957
).
Google Scholar
 
11.
Mishra
,
R. S.
, “
Solutions of Gauge-invariant generalization of field theories with asymmetric fundamental tensor
,”
Q. J. Math.
https://doi.org/10.1093/qmath/14.1.81
 
14
,
81
(
1963
).
Google Scholar
Crossref
Search ADS
 
© 2008 American Institute of Physics.
2008
American Institute of Physics
You do not currently have access to this content.