Keywords
Klein-Gordon
general relativity
Schwarzschild
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Abstract
The behaviour of a massive complex Klein-Gordon scalar field in a Schwarzschild background is analized using tortoise coordinates. Using these coordinates we obtain an expression for the action in terms of an effective potential and a radial wave function. From the action we get the corresponding wave equation and obtain some solutions of that equation for a mode of frequency u. Additionally, we study the effective potential in terms of the radial distance r and the quantum number l. Finally, we estimate the energy that we need to traverse the potential barrier for some values of l.
References
Ludvigsen, M. 1999. "General Relativity A Geometric Approach", Cambridge University Press, Cambridge, UK.
Kenyon, I. 1996. "General Relativity", Oxford University Press, Oxford, UK.
Marín, C. 2007. "La Expansión del Universo", Una Introducción a Cosmología, Relatividad General y Física de Partículas, USFQ, Quito - Ecuador.
Ohanian, H. 1976. "Gravitation and Spacetime", W. W. Norton & Company, Inc.
Misner, C.; Thorne, K.; Wheeler, J. 1973. "Gravitation", W. H. Freeman & Company, NY.
Cheng, T. 2005. "Relativity, Gravitation and Cosmology, A Basic Introduction", Oxford University Press, Oxford, UK.
Ryder, L. 1991. "Quantum Field Theory", Cambridge University Press, Cambridge, UK.
Kaku, M. 1993. "Quantum Field Theory, A Modern Introduction", Oxford University Press, Oxford, UK.
Halzen, F.; Martin, A. 1984. "Quarks and Leptons", John Wiley & Sons.
Susskind, L.; Lindesay, J. 2005. "An Introduction to Black Holes, Information and the String Theory Revolution, The Holographic Universe", World Scientific Publishing.
Arfken, G.; Weber, H. 2005. "Mathematical Methods for Physicists", Sixth Edition, Academic Press.
Riley, K.; Hobson, M.; Bence, S. 2006. "Mathematical Methods for Physics and Engineering", Third Edition, Cambridge University Press, Cambridge, UK.
Hobson, M.; Efstathiou, G.; Lasenby, A. 2006. "General Relativity, An Introduction for Physicists", Cambridge University Press, Cambridge, UK.
Spiegel, M.; Rapun, L. 1988. "Fórmulas y Tablas de Matemática Aplicada", Mc Graw Hill.
Beyer, W. 1991. "Standard Mathematical Tables and Formulae", 29th Edition, CRC Press.