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arXiv 2602.02069nucl-thgr-qchep-ph
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中微子星属性的通用关系与相关性分析：在能量动量平方引力中

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

National Institute of Technology, Rourkela（鲁尔基拉国家理工学院）

Sayantan Ghosh

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AI总结：

本研究在能量动量平方引力框架下，分析中微子星属性的通用关系与相关性，探讨不同参数对宏观属性的影响。

摘要：

中微子星（PNSs）是超新星核心塌缩后的高温、富含轻子的残余物，经历冷却阶段后成为冷稳定的中子星（NSs）。由于PNSs也是具有强引力场的超致密物体，我们可以用它们探测广义相对论（GR）在高曲率区域的情况，类似于NSs。在本研究中，我们利用四种不同的相对论平均场（RMF）方程（EOSs）分析PNSs的宏观属性，如质量、半径、紧凑性、潮汐变形性、f-模振荡和引力束缚能。固定每个重子的熵（S=1, 2）并改变轻子分数（Y_l）。S和Y_l的变化对这些属性有显著影响。在GR之外扩展我们的研究，我们探索这些影响在能量动量平方引力（EMSG）框架下的情况。这种修正的引力理论在场方程中加入平方能量动量项，并引入一个自由参数α。在弱场区域，EMSG与GR无法区分，但在强场区域，如PNSs或NSs，它显示出可测量的偏差。改变自由参数α，我们观察到PNSs的宏观属性有显著变化。之后，我们专注于宏观属性的通用关系和通用关系的相关性。我们发现，尽管S、Y_l和α的变化显著改变了宏观属性，但相关性仍然很强且几乎不受影响。

英文摘要：

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 $α$. 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. 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 $α$, the correlations remain strong and nearly unaffected.

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