Relativistic formalism for computation of irrotational binary stars in quasiequilibrium states

Masaru Shibata

doi:10.1103/PhysRevD.58.024012

Access by Xinjiang University

Relativistic formalism for computation of irrotational binary stars in quasiequilibrium states

Masaru Shibata

Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

PDF

Phys. Rev. D 58, 024012 – Published 24 June, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.024012

Abstract

We present relativistic hydrostatic equations for obtaining irrotational binary neutron stars in quasiequilibrium states in the $3 + 1$ formalism. The equations derived here are different from those previously given by Bonazzola, Gourgoulhon, and Marck, and have a simpler and more tractable form for computation in numerical relativity. We also present hydrostatic equations for computation of equilibrium irrotational binary stars in the first post-Newtonian order.

References (19)

A. Abramovici et al., Science 256, 325 (1992).
C. Bradaschia et al., Nucl. Instrum. Methods Phys. Res. A 289, 518 (1990).
J. Hough, in Proceedings of the Sixth Marcel Grossmann Meeting, edited by H. Sato and T. Nakamura (World Scientific, Singapore, 1992), p. 192.
K. Kuroda et al., in Proceedings of the International Conference on Gravitational Waves: Sources and Detectors, edited by I. Ciufolini and F. Fidecard (World Scientific, Singapore, 1997), p. 100.
For example, K. S. Thorne, in Proceeding of Snowmass 94 Summer Study on Particle and Nuclear Astrophysics and Cosmology, edited E. W. Kolb and R. Peccei (World Scientific, Singapore, 1995), and references cited therein.
L. Lindblom, Astrophys. J. 398, 569 (1992).
M. Shibata, Phys. Rev. D 55, 6019 (1997); Prog. Theor. Phys. 96, 317 (1996); M. Shibata, K. Taniguchi, and T. Nakamura, Prog. Theor. Phys. Suppl. 128, 295 (1997).
T. W. Baumgarte, G. B. Cook, M. A. Scheel, S. L. Shapiro, and S. A. Teukolsky, Phys. Rev. Lett. 79, 1182 (1997); Phys. Rev. D 57, 7299 (1998).
However, for Newtonian case, the following researchers have obtained irrotational Newtonian equilibrium states: K. Uryu and Y. Eriguchi, Mon. Not. R. Astron. Soc. 296, L1 (1998); S. Bonazzola, E. Gourgoulhon, and J.-A. Marck, presented at GRG 15, India, 1997.
C. S. Kochanek, Astrophys. J. 398, 234 (1992); ibid.L. Bildsten and C. Cutler, 400, 175 (1992).
S. Bonazzola, E. Gourgoulhon, and J.-A. Marck, Phys. Rev. D 56, 7740 (1997).
S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-time (Cambridge University Press, Cambridge, England, 1973), p. 84.
A. P. Lightman, W. H. Press, R. H. Price, and S. A Teukolsky, Problem Book in Relativity and Gravitation (Princeton University Press, Princeton, NJ, 1975), problem 16.17.
S. Chandrasekhar, Astrophys. J. 148, 621 (1967).
S. Chandrasekhar, Astrophys. J. 142, 1488 (1965): L. Blanchet, T. Damour, and G. Schäfer, Mon. Not. R. Astron. Soc. 242, 289 (1990).
K. Taniguchi and M. Shibata, Phys. Rev. D 56, 798 (1997).
M. Shibata and K. Taniguchi, Phys. Rev. D 56, 811 (1997).
S. A. Teukolsky, gr-qc/9803082.
E. Gourgoulhon, gr-qc/9804054.

[c1] A. Abramovici et al., Science 256, 325 (1992).

[c2] C. Bradaschia et al., Nucl. Instrum. Methods Phys. Res. A 289, 518 (1990).

[c3] J. Hough, in Proceedings of the Sixth Marcel Grossmann Meeting, edited by H. Sato and T. Nakamura (World Scientific, Singapore, 1992), p. 192.

[c4] K. Kuroda et al., in Proceedings of the International Conference on Gravitational Waves: Sources and Detectors, edited by I. Ciufolini and F. Fidecard (World Scientific, Singapore, 1997), p. 100.

[c5] For example, K. S. Thorne, in Proceeding of Snowmass 94 Summer Study on Particle and Nuclear Astrophysics and Cosmology, edited E. W. Kolb and R. Peccei (World Scientific, Singapore, 1995), and references cited therein.

[c6] L. Lindblom, Astrophys. J. 398, 569 (1992).

[c7] M. Shibata, Phys. Rev. D 55, 6019 (1997); Prog. Theor. Phys. 96, 317 (1996); M. Shibata, K. Taniguchi, and T. Nakamura, Prog. Theor. Phys. Suppl. 128, 295 (1997).

[c8] T. W. Baumgarte, G. B. Cook, M. A. Scheel, S. L. Shapiro, and S. A. Teukolsky, Phys. Rev. Lett. 79, 1182 (1997); Phys. Rev. D 57, 7299 (1998).

[c9] However, for Newtonian case, the following researchers have obtained irrotational Newtonian equilibrium states: K. Uryu and Y. Eriguchi, Mon. Not. R. Astron. Soc. 296, L1 (1998); S. Bonazzola, E. Gourgoulhon, and J.-A. Marck, presented at GRG 15, India, 1997.

[c10] C. S. Kochanek, Astrophys. J. 398, 234 (1992); ibid.L. Bildsten and C. Cutler, 400, 175 (1992).

[c11] S. Bonazzola, E. Gourgoulhon, and J.-A. Marck, Phys. Rev. D 56, 7740 (1997).

[c12] S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-time (Cambridge University Press, Cambridge, England, 1973), p. 84.

[c13] A. P. Lightman, W. H. Press, R. H. Price, and S. A Teukolsky, Problem Book in Relativity and Gravitation (Princeton University Press, Princeton, NJ, 1975), problem 16.17.

[c14] S. Chandrasekhar, Astrophys. J. 148, 621 (1967).

[c15] S. Chandrasekhar, Astrophys. J. 142, 1488 (1965): L. Blanchet, T. Damour, and G. Schäfer, Mon. Not. R. Astron. Soc. 242, 289 (1990).

[c16] K. Taniguchi and M. Shibata, Phys. Rev. D 56, 798 (1997).

[c17] M. Shibata and K. Taniguchi, Phys. Rev. D 56, 811 (1997).

[c18] S. A. Teukolsky, gr-qc/9803082.

[c19] E. Gourgoulhon, gr-qc/9804054.

Physical Review D

Export citation

Export citation

Relativistic formalism for computation of irrotational binary stars in quasiequilibrium states

Abstract

References (19)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation