Quick Search:
Prog. Theor. Phys. Supplement No.70 (1981) pp. 215-237
Multi-Soliton Solutions of the Einstein Equation and the Tomimatsu-Sato Metric
Akira Tomimatsu and
Humitaka Sato*
Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima 725
*Research Institute for Fundamental Physics, Kyoto University, Kyoto 606
(Received August 10, 1981)
Abstract:
We present a new recognition about the Tomimatsu-Sato metric through reviewing the recent study of the stationary and axially symmetric Einstein field equation. We describe some powerful methods of solving the Einstein equation; the Backlund transformation, the inverse scattering method and any other. These methods derive the so-called multi-soliton solution, which represents the Kerr-NUT metric or a non-linear superposition of several Kerr-NUT metrics aligned along their common rotational axis. The Tomimatsu-Sato metric of δ = N is constructed via a limiting process that the N Kerr metrics with the same mass and angular momentum approach mutually towards their complete overlapping. We investigate the space-time properties of the multi-soliton metric, by taking the two Kerr case as a typical example.
URL :
http://ptp.ipap.jp/link?PTPS/70/215/
DOI : 10.1143/PTPS.70.215
References:
-
B. Carter, Phys. Rev. Lett. 26 (1971), 331[APS].
D. C. Robinson, Phys. Rev. Lett. 34 (1975), 905[APS].
-
On simple models of collapses generating naked singularities, see, P. Yodzis, H. J. Seifert and H. M. zum Hagen, Commun. Math. Phys. 34 (1973), 135[CrossRef].
E. P. T. Liang, Phys. Rev. D 10 (1974), 447[APS].
-
A. Tomimatsu and H. Sato, Phys. Rev. Lett. 29 (1972), 1344[APS]; Prog. Theor. Phys. 50 (1973), 95[PTP].
For a concise closed form of the T-S metric with an arbitrary positive integer parameter δ, see,
M. Yamazaki, Prog. Theor. Phys. 57 (1977), 1951[PTP];
J. Math. Phys. 18 (1977), 2502[CrossRef].
-
R. P. Kerr, Phys. Rev. Lett. 11 (1963), 237[APS].
-
W. Kinnersley, J. Math. Phys. 18 (1977), 1529[AIP Scitation].
-
W. Kinnersley and D. M. Chitre, J. Math. Phys. 18 (1977), 1538[CrossRef];
ibid. 19 (1978), 1926[CrossRef];
ibid. 19 (1978), 2037[CrossRef].
-
G. Neugebauer, J. of Phys. A 12 (1979), L67[CrossRef].
- V. A. Belinsky and V. E. Zakharov, Sov. Phys. JETP 48 (1978), 985; ibid. 50 (1979), 1.
-
F. J. Ernst, Phys. Rev. 167 (1968), 1175[APS].
- H. Weyl, Ann. de Phys. 54 (1917), 117.
-
D. M. Zipoy, J. Math. Phys. 7 (1966), 1137[CrossRef].
-
B. H. Voorhees, Phys. Rev. D 2 (1970), 2119[APS].
-
B. K. Harrison, Phys. Rev. Lett. 41 (1978), 1197[APS];
Phys. Rev. D 21 (1980), 1695[APS].
-
M. Omote and M. Wadati, J. Math. Phys. 22 (1981), 961[AIP Scitation].
-
G. Neugebauer, J. of Phys. A 13 (1980), 1737[IoP STACKS].
-
G. Neugebauer, J. of Phys. A 13 (1980), L19[CrossRef].
-
D. Kramer and G. Neugebauer, Phys. Lett. A 75 (1980), 259[CrossRef].
-
D. Maison, Phys. Rev. Lett. 41 (1978), 521[APS];
J. Math. Phys. 20 (1979), 871[AIP Scitation].
- M. Omote and M. Wadati, Prog. Theor. Phys. 65 (1981), 1621[PTP].
- A. Tomimatsu, Prog. Theor. Phys. 63 (1980), 1054[PTP].
- K. Ueno, RIMS-345 (preprint).
- K. Ueno, RIMS Kokyuroku 414 (1981), 9.
- R. Hirota, in Lecture Notes in Math. 515, edited by A. Dold and B. Eckmann (Springer-Verlag, 1974).
-
C. M. Cosgrove, J. of Phys. A 11 (1978), 2389[CrossRef];
ibid. 11 (1978), 2405[CrossRef].
On another approach based on γ, see, A. Tomimatsu, Prog. Theor. Phys. 66 (1981), 526[PTP].
-
I. Hauser and F. J. Ernst, J. Math. Phys. 21 (1980), 1126[CrossRef].
- See, for example, H. Sato, in Physics and Astrophysics of Neutron Stars and Black Holes, edited by R. Giacconi and R. Ruffini (North Holland, 1978), p. 624.
- K. Oohara and H. Sato, Prog. Theor. Phys. 65 (1981), 1891[PTP].
