Scalar field in ReissnerNordström spacetime: Bound state and scattering state (with appendix on eliminating oscillation in partial sum approximation of periodic function)
Abstract
In this paper, we solve the massive scalar field in the ReissnerNordström spacetime. The scalar field in the ReissnerNordström spacetime has both bound states and scattering states. For bound states, we solve the boundstate wave function and the eigenvalue spectrum. For scattering states, we solve the scattering wave function and give an explicit expression for scattering phase shift by the integral equation method. Especially, we introduce the tortoise coordinate for the ReissnerNordström spacetime. Moreover, in the calculation of scattering cross sections, we encounter a difficulty in partial sum approximation. If the sum of partial waves cannot be performed exactly, one has to turn to the partial sum approximation which approximates a function by the first several terms of the series. However, in the partial sum approximation there exists an incorrect oscillation which cannot be eliminated by keeping more terms. In the appendix we suggest an approach for eliminating such oscillations in the partial sum.
 Publication:

Annals of Physics
 Pub Date:
 September 2021
 DOI:
 10.1016/j.aop.2021.168578
 arXiv:
 arXiv:1902.01054
 Bibcode:
 2021AnPhy.43268578L
 Keywords:

 ReissnerNordström spacetime;
 Massive scalar field;
 Boundstate eigenfunction and eigenvalue;
 Scattering wave function and phase shift;
 Integral equation method;
 Oscillation in partial sum approximation;
 General Relativity and Quantum Cosmology
 EPrint:
 Annals of Physics 432(2021)168578