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.
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