https://doi.org/10.1140/epjp/s13360-021-01546-1
Regular Article
Mapping the Dirac equation with spin and pseudospin symmetries in curved spacetime in the non-relativistic regime
Instituto de Ciências Exatas, Universidade Federal Fluminense, 27213-145, Volta Redonda, RJ, Brazil
Received:
17
February
2021
Accepted:
7
May
2021
Published online:
14
May
2021
The Dirac equation with spin and pseudospin symmetries in curved spacetime with line element 
and electromagnetic (EM) field 
is solved exactly. For this, we map the radial spinor in the non-relativistic regime and, as an application, we considered the mapping of the Coulomb–Schrödinger problem. So, it was possible to obtain both the spin and pseudospin symmetries even in the presence of a nonzero tensor potential. The eigenenergies obtained in the relativistic regime are the same for different types of couplings of the line element with the EM field 
, i.e., we can determine a way to map the same non-relativistic problem from different relativistic systems in curved spacetime. We compare some types of couplings in graphs of the probability densities.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
