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arXiv · 1612.02644

Scattering state and bound state of scalar field in Schwarzschild spacetime: Exact solution

Wen-Du Li·Yu-Zhu Chen·Wu-Sheng Dai
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Abstract

The main aim of this paper is twofold. (1) Exact solutions of a scalar field in the Schwarzschild spacetime are presented. The exact wave functions of scattering states and bound-states are presented. Besides the exact solution, we also provide explicit approximate expressions for bound-state eigenvalues and scattering phase shifts. (2) By virtue of the exact solutions, we give a direct calculation for the discontinuous jump on the horizon for massive scalar fields, while in literature such a jump is obtained from an asymptotic solution by an analytic extension treatment.

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Wen-Du Li, Yu-Zhu Chen, Wu-Sheng Dai. 2022-01-19. Scattering state and bound state of scalar field in Schwarzschild spacetime: Exact solution. https://doi.org/10.1016/j.aop.2019.167919

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