Scattering of massive scalars by Schwarzschild black holes

Details Scattering of massive scalars by Schwarzschild black holes Scattering of massive scalars by Schwarzschild black holes

2011-06-14

arxiv.org/abs/1106.2709v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, 3 figures

Scientific paper

The Klein-Gordon equation for the wave function of a single massive scalar is written in spherical and parabolic coordinates in the presence of a Schwarzschild background, and some semi-classical techniques for deriving asymptotic results are considered. In addition to the well-known logarithmic phase shift due to the tortoise radial coordinate, it is found that there is a mass-dependent logarithmic phase shift at infinity. This is found to be necessary to match the Newtonian cross-section in the non-relativistic limit. Finally, by imposing suitable boundary conditions near the horizon, the phase shift is calculated.

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