Research and Innovation Articles
Published 2007-04-30
Keywords
- numerical relativity,
- finite difference methods,
- Einstein’s equations
How to Cite
Guzmán, F. S. (2007). Introducción a la relatividad numérica. Revista Integración, Temas De matemáticas, 25(1), 1–32. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/259
Abstract
In this manuscript there are examples of the technique of finite differences approximations to the solution of systems of partial differential equations, in particular systems of equations associated with the Einstein’s equations. The aim is that the examples that are shown can serve as an introduction to Numerical Relativity. The cases studied in depth are: the wave equation in a 1+1 general flat space-time, the real scalar field coupled to General Relativity and the complex scalar field coupled to General Relativity.
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References
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[6] Olivier Sarbach, Luis Lehner, Phys. Rev. D 71, 026002 (2005).
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[16] M. Alcubierre, J.A. González, M. Salgado, Phys. Rev. D 70, 064016 (2004).
[17] M.W. Choptuik, Phys. Rev. Lett. 70, 9-12 (1993).
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[19] R. Ruffini, S. Bonazolla, Phys. Rev. 187, 1767 (1969).
[20] E. Seidel, W-M. Suen, Phys. Rev. D 42, 384 (1990).
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[25] F.E. Schunck, D.F. Torres, Int. J. Mod. Phys. D 9, (2000) 601.
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[28] D.F. Torres, S. Capozziello, G. Lambiase, Phys. Rev. D 62, 104012 (2000).
[29] D.F. Torres, Nucl. Phys. B 26, 377 (2002).
[30] Y-F. Tuan, R. Narayan, M.J. Rees, ApJ 606, 1112 (2004).
[31] J. Balakrishna, R. Bondarescu, G. Daues, F.S. Guzmán, E. Seidel, Class. Quantum Grav. 23, 2631-2652 (2006).
[32] José A. Font, “Numerical Hydrodynamics in General Relativity”, Living Rev. Relativity 6, (2003). http://www.livingreviews.org/lrr-2003-4
[33] Gregory B. Cook, “Initial Data for Numerical Relativity”, Living Rev. Relativity 3, (2000). http://www.livingreviews.org/lrr-2000-5
[34] José María Martí, Ewald Müller, “Numerical Hydrodynamics in Special Relativity”, Living Rev. Relativity 6, (2003). http://www.livingreviews.org/lrr-2003-7
[35] Peter Anninos, “Computational Cosmology: from the Early Universe to the Large Scale Structure”, Living Rev. Relativity 1, (1998). http://www.livingreviews.org/lrr-1998-2
[36] M. Alcubierre, Introduction to 3+1 Numerical Relativity. Oxford University Press, 2008.