Exploring the macroscopic properties of proto-neutron stars: Effects of entropy and lepton fraction

Neutron stars (NSs) have generally been considered as cold, zero-temperature entities. Recent progress in computational methods and theoretical modelling has opened up the exploration of finite temperature effects, marking an important research frontier. We examine the macroscopic properties of Proto-Neutron Stars (PNS) using different parametrizations of relativistic mean field (RMF) models. We adopt a constant entropy approach by fixing entropy per baryon, $S=1$ and 2. Higher S elevates the maximum mass for PNS and flattens the mass-radius curves. The higher lepton fraction ($Y_l$) leads to a decrease in maximum mass and an increase in the canonical radius. Furthermore, both the S and $Y_l$ influence the dimensionless tidal deformability (Λ). We note that the f-mode frequencies in PNSs increase as S decreases and the $Y_l$ increases at maximum mass. We find that the macroscopic properties of the PNS exhibit the same trend, irrespective of the parameter sets employed for the variation of S and $Y_l$.