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Prog. Theor. Phys. Supplement No.70 (1981) pp. 202-214
Numerical Relativity
Takashi Nakamura
Research Institute for Fundamental Physics, Kyoto University, Kyoto 606
(Received September 2, 1981)
Abstract:
The recent development in Numerical Relativity is reviewed. Important problems which numerical relativity should treat are 1) the final structure of space-time, 2) generation of gravitational waves, 3) supernova explosions, 4) formation of supermassive black holes and 5) cosmology. The present status on each problem is discussed in §1. In §2, various formalisms of the Einstein equations, coordinate conditions and numerical methods are compared. In §3, numerical examples of collapse of rotating stars are shown.
URL :
http://ptp.ipap.jp/link?PTPS/70/202/
DOI : 10.1143/PTPS.70.202
References:
-
J. R. Oppenheimer and H. Snyder, Phys. Rev. 56 (1939), 455[APS].
-
M. M. May and R. H. White, Phys. Rev. 141 (1966), 1232[APS]; Meth. Comp. Phys. 7 (1969), 219.
- T. Matsuda and H. Sato, Prog. Theor. Phys. 41 (1969), 1021[PTP].
- L. Smarr, Ann. N. Y. Acad. Sci. 302 (1977), 569.
L. Smarr, A. Cadez, B. Dewitt and K. Eppley, Phys. Rev. D 14 (1970), 2443[APS].
L. Smarr, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 245.
- For example S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-time (Cambridge University Press, 1973).
R. Penrose, Proceedings of the First Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini (North-Holland, Amsterdam, 1977).
-
W. Israel, Phys. Rev. 164 (1967), 1776[APS].
B. Carter, Phys. Rev. Lett. 26 (1971), 331[APS].
-
D. C. Robinson, Phys. Rev. Lett. 34 (1975), 905[APS].
- For example,
W. Kinnersley and D. M. Chitre, J. Math. Phys. 19 (1978), 2037[CrossRef].
C. Hoenselaers, W. Kinnersley and B. C. Xanthopoulos, Phys. Rev. Lett. 42 (1979), 481[APS].
D. Kramer and G. Neugebauer, Phys. Lett. A 75 (1980), 259[CrossRef].
M. Yamazaki, Prog. Theor. Phys. 64 (1980), 861[PTP].
-
A. Tomimatsu and H. Sato, Phys. Rev. Lett. 29 (1972), 1344[APS]; Prog. Theor. Phys. 50 (1973), 95[PTP].
-
P. Yodzis, H. J. Seifert and Muller and Muller zum Hagen, Commun. Math. Phys. 34 (1973), 135[CrossRef].
- T. Nakamura, K. Maeda, S. Miyama and M. Sasaki, Proceedings of the Second Marcel Grossmann Meeting on General Relativity (North Holland, Amsterdam, 1980).
- T. Nakamura and H. Sato, to be submitted to Prog. Theor. Phys.
- T. Nakamura, Prog. Theor. Phys. 65 (1981), 1876[PTP].
- T. Nakamura and H. Sato, Prog. Theor. Phys. 66 (1981), 2038[PTP].
-
T. Nakamura and H. Sato, Phys. Lett. A 86 (1981), 318[CrossRef].
- M. Sasaki, K. Maeda, S. Miyama and T. Nakamura, Prog. Theor. Phys. 63 (1980), 1051[PTP].
- S. L. Shapiro and S. A. Teukolsky, Astrophys. J. 235 (1980), 199.
- G. Pizzella, Lecture given at the Second Marcel Grossmann Meeting, Trieste, July 1979.
- T. X. Thuan and J. P. Ostriker, Astrophys. J. 191 (1974), L105.
R. Epstein and R. V. Wagoner, Astrophys. J. 197 (1975), 717[CrossRef].
I. D. Novikov, Sov. Astron. (A. J.) 19 (1975), 398.
M. S. Turner and R. V. Wagoner, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 383.
S. L. Shapiro, Astrophys. J. 214 (1977), 566[CrossRef].
R. A. Saenz and S. L. Shapiro, Astrophys. J. 221 (1978), 286[CrossRef].
S. L. Shapiro, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 355.
R. A. Saenz and S. L. Shapiro, Astrophys. J. 229 (1979), 1107[CrossRef].
-
M. Davis, R. Ruffini, W. H. Press and R. H. Price, Phys. Rev. Lett. 27 (1971), 1466[APS].
M. Davis, R. Ruffini and J. Tiomno, Phys. Rev. D 5 (1971), 2932[APS].
M. Davis and R. Ruffini, Lett. Nuovo Cim. 2 (1971), 1165.
R. Ruffini, Phys. Rev. D 7 (1973), 972[APS].
S. L. Detweiler, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 211.
S. L. Detweiler and E. Szedenits, Astrophys. J. 231 (1979), 211[CrossRef].
-
C. T. Cunningham, R. H. Price and V. Moncrief, Astrophys. J. 224 (1978), 643[CrossRef];
ibid. 230 (1979), 870[CrossRef].
- K. Eppley, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 275.
S. Miyama, Prog. Theor. Phys. 65 (1981), 894[PTP].
- J. R. Wilson, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 423.
-
T. Nakamura and M. Sasaki, Phys. Lett. B 106 (1981), 69[CrossRef]; to be submitted to Prog. Theor. Phys.
-
S. A. Colgate and R. H. White, Astrophys. J. 143 (1966), 626[CrossRef].
-
W. D. Arnett, Astrophys. J. 218 (1977), 815[CrossRef].
J. R. Wilson, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 335.
-
K. A. Van Ripper Astrophys. J. 232 (1979), 558[CrossRef].
-
D. Q. Lamb, J. M. Lattimer, C. J. Pethick and D. G. Ravenhall, Phys. Rev. Lett. 41 (1978), 1623[APS].
-
J. M. LeBlanc and J. R. Wilson, Astrophys. J. 161 (1970), 541[CrossRef].
- D. L. Meier, R. I. Epstein, W. D. Arnett and D. N. Schramm, Astrophys. J. 204 (1976), 869.
-
J. H. Lacy, F. Baas, C. H. Townes and T. R. Geballe, Astrophys. J. 227 (1979), L17[CrossRef].
-
P. J. Young, J. A. Westphal, J. Kristian, C. P. Wilson and F. P. Landauer, Astrophys. J. 221 (1978), 721[CrossRef].
P. J. Young, W. L. W. Sargent, J. Kristian and J. A. Westphal, Astrophys. J. 234 (1979), 76[CrossRef].
-
D. Lynden-Bell, Nature 223 (1969), 690[CrossRef].
- For example,
J. E. Pringle, M. J. Rees and A. G. Pacholczyk, Astron. Astrophys. 29 (1973), 179.
D. Lynden-Bell and M. J. Rees, Mon. Not. R. Astron. Soc. 152 (1971), 461.
F. Takahara, Prog. Theor. Phys. 60 (1978), 1606[PTP]; ibid. 62 (1979), 629[PTP].
F. Takahara, S. Tsuruta and S. Ichimaru, submitted to Astrophys. J.
-
L. Spitzer and W. C. Saslaw, Astrophys. J. 143 (1966), 400[CrossRef].
L. Spitzer and M. E. Stone, Astrophys. J. 147 (1967), 519[CrossRef].
- M. C. Begelman and M. J. Rees, Mon. Not. R. Astron. Soc. 185 (1978), 847.
- F. Hoyle and W. A. Fowler, Mon. Not. R. Astron. Soc. 125 (1963), 169;
Nature 197 (1963), 533[CrossRef].
- W. A. Fowler, “High-Energy Astrophysics”, Proceedings of the International School of Physics “Enrico Fermi” Course XXXV, ed. L. Gratton (Academic Press, New York, 1966), p. 313.
- L. M. Ozernoi and V. W. Usov, Astrophys. Space Sci. 25 (1973), 531.
-
P. Morrison, Astrophys. J. 157 (1969), L73[CrossRef].
- J. R. Wilson, “Physics and Astrophysics of Neutron Stars and Black Holes", Proceedings of the International School of Physics "Enrico Fermi” Course LXV, ed. R. Giacconi and R. Ruffini (North-Holland, Amsterdam, 1978), p. 644.
-
K. J. Fricke, Astrophys. J. 189 (1974), 535[CrossRef].
- D. S. De Young, Ann. Rev. Astron. Astrophys. 14 (1976), 447.
- S. Ikeuchi, Publ. Astron. Soc. Jpn. 33 (1981), No. 2.
J. P. Ostriker and I. L. Cowie, Astrophys. J. 243 (1981), L127[CrossRef].
- S. Ikeuchi, private communication.
- I. D. Novikov and A. G. Polnarev, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 173.
- J. Centrella, Astrophys. J. 241 (1980), 875.
- K. Tomita, Prog. Theor. Phys. 48 (1972), 78[PTP].
- J. Pachner, Gravitation, Quanta and the Universe, ed. A. R. Prasanna (Willey, Eastern, 1980) and references therein.
-
R. A. d'Inverno and J. Smallwood, Phys. Rev. D 22 (1980), 1233[APS].
R. A. d'Inverno and J. Stachel, J. Math. Phys. 19 (1978), 2447[AIP Scitation].
- R. Arnowitt, S. Deser and C. W. Misner, “The Dynamics of General Relativity” in Gravitation; An Introduction to Current Research, ed. L. Witten (Wiley, New York, 1962), p. 227.
- K. Maeda, M. Sasaki, T. Nakamura and S. Miyama, Prog. Theor. Phys. 63 (1980), 719[PTP].
-
R. Geroch, J. Math. Phys. 12 (1971), 918[CrossRef].
-
F. Estabrook et al., Phys. Rev. D 7 (1973), 2814[APS].
-
L. Smarr and J. W. York, Jr., Phys. Rev. D 17 (1978), 1945[APS].
-
N. O'Murchadha and J. W. York, Jr., J. Math. Phys. 14 (1973), 1551[CrossRef].
- T. Nakamura, K. Maeda, S. Miyama and M. Sasaki, Prog. Theor. Phys. 63 (1980), 1229[PTP].
- T. Piran, to be published in Math. Compt. Phys.
- T. Piran, Sources of Gravitational Radiation, ed. L. Smarr (Cambridge University Press, 1979), p. 409.
T. Piran, to appear in Recent Developments in General Relativity, ed. R. Ruffini; to appear in Essays in General Relativity; A Festshrift for Abraham Taub.
- T. Nakamura, to be submitted to Astrophys. Space Sci.
-
T. Piran, Phys. Rev. Lett. 41 (1978), 1085[APS].
Citing Article(s) :
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Progress of Theoretical Physics Vol. 70 No. 4 (1983) pp. 1144-1147
:
-
General Relativistic Collapse of Accreting Neutron Stars with Rotation
-
Takashi Nakamura