TY - JOUR
T1 - Klein-Gordon equation in curved space-time
AU - Lehn, R. D.
AU - Chabysheva, Sophia S
AU - Hiller, John R
N1 - Publisher Copyright:
© 2018 European Physical Society.
PY - 2018/5/17
Y1 - 2018/5/17
N2 - We report the methods and results of a computational physics project on the solution of the relativistic Klein-Gordon equation for a light particle gravitationally bound to a heavy central mass. The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. Metrics are considered for an impenetrable sphere, a soft sphere of uniform density, and a soft sphere with a linear transition from constant to zero density; in each case the radius of the central mass is chosen to be sufficient to avoid any event horizon. The solutions are obtained numerically and compared with nonrelativistic Coulomb-type solutions, both directly and in perturbation theory, to study the general-relativistic corrections to the quantum solutions for a 1/r potential. The density profile with a linear transition is chosen to avoid singularities in the wave equation that can be caused by a discontinuous derivative of the density. This project should be of interest to instructors and students of computational physics at the graduate and advanced undergraduate levels.
AB - We report the methods and results of a computational physics project on the solution of the relativistic Klein-Gordon equation for a light particle gravitationally bound to a heavy central mass. The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. Metrics are considered for an impenetrable sphere, a soft sphere of uniform density, and a soft sphere with a linear transition from constant to zero density; in each case the radius of the central mass is chosen to be sufficient to avoid any event horizon. The solutions are obtained numerically and compared with nonrelativistic Coulomb-type solutions, both directly and in perturbation theory, to study the general-relativistic corrections to the quantum solutions for a 1/r potential. The density profile with a linear transition is chosen to avoid singularities in the wave equation that can be caused by a discontinuous derivative of the density. This project should be of interest to instructors and students of computational physics at the graduate and advanced undergraduate levels.
KW - Klein-Gordon equation
KW - computational physics
KW - gravitational binding
KW - static spherical space-times
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U2 - 10.1088/1361-6404/aabdde
DO - 10.1088/1361-6404/aabdde
M3 - Article
AN - SCOPUS:85050069710
SN - 0143-0807
VL - 39
JO - European Journal of Physics
JF - European Journal of Physics
IS - 4
M1 - 045405
ER -