Quadrupolar gravitational fields described by the q-metric
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Keywords:
Quadrupole moment, naked singularities, q-metric.Abstract
We investigate the Zipoy-Voorhees metric ( q - metric) as the simplest static, axially symmetric solution of Einstein’s vacuum field equations that possesses as independent parameters the mass and the quadrupole moment. In accordance with the black holes uniqueness theorems, the presence of the quadrupole completely changes the geometric properties of the corresponding spacetime that turns out to contain naked singularities for all possible values of the quadrupole parameter. The naked singularities, however, can be covered by interior solutions that correspond to perfect fluid sources with no specific equations of state. We conclude that the q - metric can be used to describe the entire spacetime generated by static deformed compact objects.References
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2 B. Voorhees, Phys. Rev. D 2 (1970) 2119.
3 H. Stephani, D. Kramer, M. A. H.
MacCallum, C. Hoenselaers, and E. Herlt, Exact
Solutions of Einstein’s Field Equations
(Cambridge University Press, Cambridge, 2003).
4 D. Papadopoulos, B. Stewart, L. Witten,
Phys. Rev. D 24 (1981) 320.
5 L. Herrera and J. L. Hernandez-Pastora, J.
Math. Phys. 41 (2000) 7544.
6 L. Herrera, G. Magli and D. Malafarina,
Gen. Rel. Grav. 37 (2005) 1371.
7 N. Dadhich and G. Date, (2000), arXvi:grqc/
0012093
8 H. Kodama and W. Hikida, Class.
Quantum Grav. 20 (2003) 5121.
9 H. Quevedo, Int. J. Mod. Phys. 20 (2011)
1779.
10 J. L. Synge, Relativity: The General
Theory (North-Holland, Amsterdam, 1960).
11 H. Quevedo, Forts. Physik 38 (1990) 733.
12 R. Geroch, J. Math. Phys. 11 (1970) 1955;
J. Math. Phys. 11 (1970) 2580.
13 H. Quevedo, Multipolar Solutions, in
Proceedings of the XIV Brazilian School of
Cosmology and Gravitation, (2012);
arXiv:1201.1608
14 K. Boshkayev, H. Quevedo, and R.
Ruffini, Phys. Rev. D 86:064403 (2012).
15 D. Malafarina, Conf. Proc. C0405132
(2004) 273.
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How to Cite
Quevedo, H., Toktarbay, S., & Aimuratov, Y. (2012). Quadrupolar gravitational fields described by the q-metric. International Journal of Mathematics and Physics, 3(2), 133–139. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/56
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Theoretical Physics and Plasma Physics
