Universal Relations and Correlation Analysis of Proto-Neutron Star Properties in Energy-Momentum Squared Gravity

Abstract

Proto-neutron stars (PNSs) are the hot, lepton-rich remnants of the core collapse supernovae, which go through a cooling phase and become cold, stable Neutron stars (NSs). Since PNSs are also superdense objects with strong gravitational fields, we can use them to probe general relativity (GR) in the high-curvature regime, similar to NSs. In this study, we analyze the macroscopic properties of PNSs using three different relativistic mean-field (RMF) equations of state (EOSs) with fixed entropy per baryon (S =1, 2) and varying the lepton fractions (Yl). Higher S values increase the mass and flatten the mass-radius relation, and higher Yl values decrease the maximum mass and increase the canonical radius. The variation of S and Yl affects the f-mode oscillation frequency, tidal deformability, moment of inertia and the surface curvature of the PNS. Extending our study beyond GR, we explore these effects within the framework of Energy-Momentum Squared Gravity (EMSG), a modified gravity theory that adds the nonlinear energy-momentum terms to the field equations. In the weak-field regimes, EMSG remains indistinguishable from GR, but in the strong-field regimes, such as PNSs or NSs, it shows measurable deviations. Varying the free parameter α, we observe significant changes in the macroscopic properties of the PNSs.