IntroductionThis paper investigates the impact of differential rotation on the bulk properties and onset of rotational instabilities in neutron stars at finite temperatures up to 50 MeV.MethodsUtilizing the relativistic Brueckner-Hartree-Fock (RBHF) formalism in full Dirac space, the study constructs equation of state (EOS) models for hot neutron star matter, including conditions relevant for high temperatures. These finite-temperature EOS models are applied to compute the bulk properties of differentially rotating neutron stars with varying structural deformations.ResultsThe findings demonstrate that the stability of these stars against bar-mode deformation, a key rotational instability, is only weakly dependent on temperature. Differential rotation significantly affects the maximum mass and radius of neutron stars, and the threshold for the onset of bar-mode instability shows minimal sensitivity to temperature changes within the examined range.DiscussionThese findings are crucial for interpreting observational data from neutron star mergers and other high-energy astrophysical events. The research underscores the necessity of incorporating differential rotation and finite temperature effects in neutron star models to predict their properties and stability accurately.