Janis and Newman have proposed definitions of multipole moments of axially symmetric gravitational fields in terms of the initial data on a characteristic surface. This paper extends their definitions to source distributions without symmetry by considering the electromagnetic and linear gravitational fields. The global definition of four‐momentum agrees, for sandwich waves, with the objects constructed by Mo/ller and Cornish in their attempts to provide a local definition of four‐momentum.

1.
R.
Sachs
and
P. G.
Bergmann
,
Phys. Rev.
112
,
674
(
1958
).
2.
A. I.
Janis
and
E. T.
Newman
,
J. Math. Phys.
6
,
902
(
1965
). Hereinafter referred to as JN.
3.
F. A. E.
Pirani
,
Acta Phys. Polon.
15
,
389
(
1956
).
4.
H.
Bondi
,
M. G. J.
van der Burg
, and
A. W. K.
Metzner
,
Proc. Roy. Soc. (London)
A269
,
21
(
1962
).
5.
E. T. Newman (private communication). U(1) is the unitary group in one dimension (the group of phase transformations).
6.
C.
Møller
,
Kgl. Danske Videnskab. Selskab Mat. Fys. Medd.
34
, No.
3
(
1964
).
7.
F. H. J.
Cornish
,
Proc. Roy. Soc. (London)
A286
,
270
(
1965
).
8.
E.
Newman
and
R.
Penrose
,
J. Math. Phys.
3
,
566
(
1962
).
9.
Contrary to previous assertions this does not exclude incoming radiation fields. The subsequent angular considerations do, however, restrict the results to outgoing radiation fields in the linear theory.
10.
H. Bateman, Partial Differential Equations of Mathematical Physics, (Cambridge University Press, Cambridge, England, 1932).
11.
I owe this suggestion to R. Penrose. An alternative name could be the associated spherical harmonics of first order since they are analogous to the associated Legendre polynomials of first order in axially symmetric theory.
12.
These can be regarded as the field equations of Cμνρσ.
13.
E. T.
Newman
and
T. W. J.
Unti
,
J. Math. Phys.
3
,
891
(
1962
).
14.
R. K.
Sachs
,
Phys. Rev.
128
,
2851
(
1962
).
This content is only available via PDF.
You do not currently have access to this content.