  We investigated the impact of Non-Hermitian gravitational potentials on the
spatial distribution of Bose-Einstein condensate (BEC) wave functions. Through
numerical solutions of the Gross-Pitaevskii (GP) equation, we observed that the
imaginary component of Non-Hermitian gravitational potentials affects the
spatial periodicity of the BEC wave function phase, resulting in spatial
displacement of the wave function's peak. By formulating equations describing
the momentum of the BEC wave function with respect to Non-Hermitian
gravitational potential parameters and solving and analyzing them under
specific conditions, we provided a reasoned interpretation of the numerical
results. Our findings contribute to exploring the physical essence of
Non-Hermitian gravitational potentials and their impact on BEC, offering
theoretical guidance for potential related experiments.
