No Access

BUCHDAHL-LIKE TRANSFORMATIONS FOR PERFECT FLUID SPHERES

School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, PO Box 600, Wellington, New Zealand

Search for more papers by this author

and

MATT VISSER

School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington, PO Box 600, Wellington, New Zealand

Search for more papers by this author

https://doi.org/10.1142/S0218271808011912Cited by:24 (Source: Crossref)

Abstract

In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007) and Phys. Rev. D76 (2006) 0440241 (gr-qc/0607001)] we have discussed several "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general-relativistic static perfect fluid spheres. Working in Schwarzschild curvature coordinates, we used these algorithmic ideas to prove several "solution-generating theorems" of varying levels of complexity. In the present article we consider the situation in other coordinate systems. In particular, in general diagonal coordinates we shall generalize our previous theorems, in isotropic coordinates we shall encounter a variant of the so-called "Buchdahl transformation," and in other coordinate systems (such as Gaussian polar coordinates, Synge isothermal coordinates, and Buchdahl coordinates) we shall find a number of more complex "Buchdahl-like transformations" and "solution-generating theorems" that may be used to investigate and classify the general-relativistic static perfect fluid sphere. Finally, by returning to general diagonal coordinates and making a suitable ansatz for the functional form of the metric components, we place the Buchdahl transformation in its most general possible setting.

Keywords:

Fluid spheres

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

H. Stephani et al. , Exact Solutions of Einstein's Field Equations ( Cambridge University Press , 2003 ) . Google Scholar
M. S. R. Delgaty and K. Lake, Comput. Phys. Commun. 115, 395 (1998), gr-qc/9809013 DOI: 10.1016/S0010-4655(98)00130-1. Web of Science, ADS, Google Scholar
M. R. Finch and J. E. F. Skea, A review of the relativistic static fluid sphere, 1998, unpublished draft. See http://www.dft.if.uerj.br/usuarios/JimSkea/papers/pfrev.ps . Google Scholar
H. A. Buchdahl, Phys. Rev. 116, 1027 (1959), DOI: 10.1103/PhysRev.116.1027. Web of Science, Google Scholar
H. A. Buchdahl, Astrophys. J. 146, 275 (1966), DOI: 10.1086/148875. Web of Science, ADS, Google Scholar
H. Bondi, Mon. Not. R. Astron. Soc. 107, 410 (1947). Web of Science, ADS, Google Scholar
H. Bondi, Mon. Not. R. Astron. Soc. 282, 303 (1964). Web of Science, Google Scholar
M. Wyman, Phys. Rev. 75, 1930 (1949), DOI: 10.1103/PhysRev.75.1930. Web of Science, Google Scholar
S. Berger, R. Hojman and J. Santamarina, J. Math. Phys. 28, 2949 (1987), DOI: 10.1063/1.527697. Web of Science, Google Scholar
D. Martin and M. Visser, Class. Quant. Grav. 20, 3699 (2003), gr-qc/0306038 DOI: 10.1088/0264-9381/20/16/311. Web of Science, ADS, Google Scholar
S. Rahman and M. Visser, Class. Quant. Grav. 19, 935 (2002), gr-qc/0103065 DOI: 10.1088/0264-9381/19/5/307. Web of Science, ADS, Google Scholar
K. Lake, Phys. Rev. D 67, 104015 (2003), gr-qc/0209104 DOI: 10.1103/PhysRevD.67.104015. Web of Science, Google Scholar
D. Martin and M. Visser, Phys. Rev. D 69, 104028 (2004), gr-qc/0306109 DOI: 10.1103/PhysRevD.69.104028. Web of Science, Google Scholar
P. Boonserm, M. Visser and S. Weinfurtner, Phys. Rev. D 71, 124037 (2005), gr-qc/0503007 DOI: 10.1103/PhysRevD.71.124037. Web of Science, ADS, Google Scholar
P. Boonserm, M. Visser and S. Weinfurtner, Phys. Rev. D 76, 044024 (2006), gr-qc/0607001 DOI: 10.1103/PhysRevD.76.044024. Web of Science, Google Scholar
P. Boonserm, "Some exact solutions in general relativity," MSc thesis, Victoria University of Wellington , gr-qc/0610149 . Google Scholar
P. Boonserm, M. Visser and S. Weinfurtner, J. Phys. Conf. Series 68, 012055 (2007), gr-qc/0609088 DOI: 10.1088/1742-6596/68/1/012055. Google Scholar
P. Boonserm, M. Visser and S. Weinfurtner, Solution generating theorems: Perfect fluid spheres and the TOV equation, in Marcel Grossmann 11th Meeting , gr-qc/0609099 . Google Scholar