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

TL;DR

This paper investigates proto-neutron star properties within Energy-Momentum Squared Gravity, analyzing how different physical parameters affect these properties and their universal relations, revealing that correlations are robust despite significant property variations.

Contribution

It extends the analysis of proto-neutron stars to Energy-Momentum Squared Gravity, demonstrating the robustness of universal relations under modified gravity and varying physical conditions.

Findings

Macroscopic properties are sensitive to entropy, lepton fraction, and gravity modifications.

Universal relations remain strong and nearly unaffected by parameter variations.

Energy-Momentum Squared Gravity introduces measurable deviations in strong-field regimes.

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 like mass, radius, compactness, tidal deformability, $f$-mode oscillations and gravitational binding energy of PNSs using four different relativistic mean-field (RMF) equations of state (EOSs) with fixed entropy per baryon ($S$ =1, 2) and varying the lepton fractions ($Y_l$). The variation of $S$ and $Y_l$ has a noticeable effect on these properties. Extending our study beyond GR, we explore these effects within the framework of Energy-Momentum Squared Gravity (EMSG). This modified gravity theory adds the squared energy-momentum terms to the field equations with a free parameter $\alpha$. 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 $\alpha$, we observe significant changes in the macroscopic properties of the PNSs. After that, we focus on the universal relations of the macroscopic properties and the correlations of the universal relations. We find that, despite significant changes in the macroscopic properties induced by the variations of $S$, $Y_l$ and $\alpha$, the correlations remain strong and nearly unaffected.