In this paper, using the Bondi coordinates, we discuss the angular momentum at null infinity in five dimensions and address the Poincare covariance of the Bondi mass and angular momentum. We also show the angular momentum loss/gain law due to gravitational waves. In four dimensions, the angular momentum at null infinity has the supertranslational ambiguity and then it is known that we cannot construct well-defined angular momentum there. On the other hand, we would stress that we can define angular momentum at null infinity without any ambiguity in higher dimensions. This is because of the nonexistence of supertranslations in higher dimensions.
REFERENCES
1.
A.
Ashtekar
and R. O.
Hansen
, J. Math. Phys.
19
, 1542
(1978
).2.
R. P.
Geroch
, “Asymptotic structure of space-time
,” in Asymptotic Structure of Space-Time
, edited by T. P.
Esposito
and L.
Witten
(Plenum
, New York
, 1977
).3.
R.
Geroch
, J. Math. Phys.
13
, 956
(1972
).4.
K.
Tanabe
, N.
Tanahashi
, and T.
Shiromizu
, J. Math. Phys.
50
, 072502
(2009
).5.
H.
Bondi
, M. G. J.
van der Burg
, and A. W. K.
Metzner
, Proc. R. Soc. London, Ser. A
269
, 21
(1962
).6.
R. K.
Sachs
, Proc. R. Soc. London, Ser. A
270
, 103
(1962
).7.
R. K.
Sachs
, Phys. Rev.
128
, 2851
(1962
).8.
R.
Penrose
, Phys. Rev. Lett.
10
, 66
(1963
).9.
E. T.
Newman
and R.
Penrose
, J. Math. Phys.
7
, 863
(1966
).10.
R.
Penrose
, Proc. R. Soc. London, Ser. A
284
, 159
(1965
).11.
R. P.
Geroch
and G. T.
Horowitz
, Phys. Rev. Lett.
40
, 203
(1978
).12.
R. P.
Geroch
and B. C.
Xanthopoulos
, J. Math. Phys.
19
, 714
(1978
).13.
S.
Hollands
and A.
Ishibashi
, J. Math. Phys.
46
, 022503
(2005
).14.
15.
A.
Ishibashi
, Class. Quantum Grav.
25
, 165004
(2008
).16.
K.
Tanabe
, N.
Tanahashi
, and T.
Shiromizu
, J. Math. Phys.
51
, 062502
(2010
).17.
S.
Hollands
and R. M.
Wald
, Class. Quantum Grav.
21
, 5139
(2004
).18.
L. A.
Tamburino
and J. H.
Winicour
, Phys. Rev.
150
, 1039
(1966
).19.
J. H.
Winicour
, J. Math. Phys.
9
, 861
(1968
)20.
C. R.
Prior
, Proc. R. Soc. London, Ser. A
354
, 379
(1977
).21.
M.
Streubel
, Gen. Relativ. Gravit.
9
, 551
(1978
).22.
J. H.
Winicour
, “Angular momentum in general relativity
,” in General Relativity and Gravitation
, edited by A.
Held
(Plenum
, New York
, 1980
), Vol. 2
.23.
R. P.
Geroch
and J.
Winicour
, J. Math. Phys.
22
, 803
(1981
).24.
T.
Dray
, and M.
Streubel
, Class. Quantum Grav.
1
, 15
(1984
).25.
T.
Harmark
, Phys. Rev. D
70
, 124002
(2004
).26.
The coefficients of the definitions are determined so that these quantities are coincide to ADM quantities at spatial infinity.
© 2011 American Institute of Physics.
2011
American Institute of Physics
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