Effects of temperature on g-mode oscillations of neutron stars

We investigate finite-temperature nuclear matter within the SU(2) chiral sigma model to construct an equation of state relevant for proto-neutron stars. By numerically solving the Tolman OV equations, we obtained macroscopic observables such as mass and radius for various entropy-per-baryon ratios. We calculate the equilibrium and adiabatic sound speeds, which encode information about the buoyancy of matter inside the star. From this, we compute the g-mode oscillation spectrum within the relativistic Cowling approximation. Our results show that the g-mode frequency is strongly influenced by both the entropy of the star and  nuclear saturation properties such as the symmetry energy slope. Finally, we discuss how these g-modes can leave characteristic signatures on the gravitational-wave signal of protoneutron stars, potentially offering a new probe of the internal composition of dense matter.