Neutron star oscillations in pseudo-Newtonian gravity

We investigate the oscillations of neutron stars using a purely Newtonian approach and three other pseudo-Newtonian formulations. Our work is motivated by fact that formulations are commonly used in core-collapse supernova (CCSN) simulations. derive solve numerically radial nonradial perturbation equations for star different combinations modified hydrodynamics gravitational potentials. pay special attention to formulation proposed recently Zha et al. [Phys. Rev. Lett. 125, 051102 (2020)] implements standard Case A effective potential CCSN simulations with an additional lapse-function correction equations. find this "Case A+lapse" can typically approximate frequency fundamental mode $1.4 M_\odot$ computed general relativity about few tens percent our chosen EOS models. For quadrupolar $f$ mode, which expected contribute strongly waves emitted from protoneutron star, A+lapse performs much better within even maximum-mass configuration relativity.