All static spherically symmetric perfect-fluid solutions of Einstein's equations

Physical Review D

Volumn 67, Issue 10, 2003, Pages

  Lake, Kayll ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; CALCULATION; ENERGY; LIQUID; MATHEMATICAL ANALYSIS; PHYSICS; PRESSURE; SHEAR STRESS; SPACE; TIME;

EID: 33750339741     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.67.104015     Document Type: Review

References (17)

1. See M. S. R. Delgaty and K. Lake, Comput. Phys. Commun. 115, 395 (1998).
2. See W. C. Hernandez and C. W. Misner, Astrophys. J. 143, 452 (1965);
3. E. Poisson and W. Israel, Phys. Rev. D 41, 1796 (1990);
4. T. Zannias, Phys. Rev. D 41, 3252 (1990);
5. S. Hayward, Phys. Rev. D 53, 1938 (1996).
6. -φ (r) is the effective potential for null geodesics [see, for example, M. Ishak, L. Chamandy, N. Neary, and K. Lake, Phys. Rev. D 64, 024005 (2001)].
7. The problem has also been reduced to a linear equation of first order by A. S. Berger, R. Hojman, and J. Santamarina, J. Math. Phys. 28, 2949 (1987). Recently G. Fodor (gr-qc/0011040) has reduced the problem to an algebraic one with integration required only for one metric function but not the physical variables ρ and p.
8. D. Pollney, N. Pelavas, P. Musgrave, and K. Lake, Comput. Phys. Commun. 115, 381 (1998).
9. 3, which gives, uniquely, the Schwarzschild interior solution. See also H. A. Buchdahl, Am. J. Phys. 39, 158 (1971).
10. See T. W. Baumgarte and A. D. Rendall, Class. Quantum Grav. 10, 327 (1993);
11. M. Mars, M. Mercè Martín-Prats, and J. M. M. Senovilla, Phys. Lett. A 218, 147 (1996).
12. See, for example, P. Musgrave and K. Lake, Class. Quantum Grav. 13, 1885 (1996).
13. At an interior boundary surface p, but not p, must be continuous. Discontinuities in ρ are associated with phase transitions, which we do not consider here. For a discussion of interior phase transitions see, for example, L. Lindblom, Phys. Rev. D 58, 024008 (1998).
14. These were first discussed (in the spherically symmetric case) by H. Bondi, Proc. R. Soc. London A281, 39 (1964)
15. S. Rahman and M. Visser, Class. Quantum Grav. 19, 935 (2002).
16. M. Wyman, Phys. Rev. 75, 1930 (1949).
17. This is a package which runs within MAPLE. It is entirely distinct from packages distributed with MAPLE and must be obtained independently. The GRTENSORII software and documentation is distributed freely on the World Wide Web from the address http://grtensor.org