Research and Innovation Articles
Published 2009-11-05
Keywords
- Classical General Relativity,
- exact solutions,
- self-gravitating system,
- Einstein equations
How to Cite
Gutiérrez-Piñeres, A. C., González, G. A., & Viña-Cervantes, V. M. (2009). A family of relativistic charged thin disks with an inner edge. Revista Integración, Temas De matemáticas, 27(2), 89–98. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/744
Abstract
A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.
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References
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[3] M. C. Begelman. Science, 300, 1898 (2003).
[4] J. P. S. Lemos and P. S. Letelier. Class. Quantum Grav., 10, L75 (1993).
5] J. P. S. Lemos and P. S. Letelier. Phys. Rev D, 49, 5135 (1994).
[6] J. P. S. Lemos and P. S. Letelier. Int. J. Mod. Phys. D, 5, 53 (1995).
[7] O. Semerák. Class. Quantum Grav., 21, 2203 (2004).
[8] G. A. González, A. C. Gutiérrez-Piñeres and V. Viña-Cervantes. “Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions”, arXiv: 0811.3869v1 (2008).
[9] G. A. González, A. C. Gutiérrez-Piñeres and V. Viña-Cervantes. AIP Conf. Proc., 1122, 284-287 (2009).
[10] F. J. Ernst. Phys. Rev., 167, 1175 (1968).
[11] F. J. Ernst. Phys. Rev., 168, 1415 (1968).
[12] H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers and E. Herlt. Exact Solutions of Einstein’s Field Equations. Cambridge University Press, 2003.
[13] A. Papapetrou and A. Hamouni. Ann. Inst. Henri Poincaré, 9, 179 (1968).
[14] A. Lichnerowicz. C.R. Acad. Sci., 273, 528 (1971).
[15] A. H. Taub. J. Math. Phys., 21, 1423 (1980).
[16] E. Israel. Nuovo Cimento, 44B, 1 (1966).
[17] E. Israel. Nuovo Cimento, 48B, 463 (1967).
[18] E. Poisson. A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics. Cambridge University Press, 2004.
[19] G. A. González and A. C. Gutiérrez-Piñeres. “Counterrotating Dust Disk Around a Schwarzschild Black Hole: New Fully Integrated Explicit Exact Solution”, arXiv: 0811.3002v1 (2008).