AI 中文总结
针对含物质拉格朗日对度规二阶导数的修改引力中物质拉格朗日选取歧义问题，研究通过放宽四速度与度规独立的假设构建自洽框架，并经天体与宇宙学场景验证可消除该歧义。
AI 中文摘要
在广义相对论（GR）中，物质密度（$\rho$）和径向压强（$p$）常被用作物质拉格朗日密度（$\mathcal{L}_{m}$），因为二者均满足热力学自洽性，且能导出相同的爱因斯坦场方程（EFE）。而建立物质与几何显式关联的新型引力模型会涉及$\mathcal{L}_{m}$对度规张量的二阶导数，因此选择$p$或$-\rho$作为$\mathcal{L}_{m}$会得到不同的有效爱因斯坦场方程。这一混淆的产生，通常是因为人们将四速度（$u_\mu$）与度规张量（$g_{\mu\nu}$）视为独立量。本文重新审视了基础理论，通过放宽该假设提出了一套自洽框架，使修改引力理论不受$\mathcal{L}_{m}$选取的影响。最后，我们在中子星与夸克星（紫外区域）、以及辐射主导（$p=\rho/3$）物态方程的宇宙学场景（红外区域）中测试了该方法，表明其可厘清引力模型中选取$\mathcal{L}_{m}$的歧义问题。
英文摘要
Matter density ($ρ$) and radial pressure ($p$) are often used as the matter Lagrangian density ($\mathcal{L}_{m}$) because both are thermodynamically consistent and produce the same Einstein field equation (EFE) in general relativity (GR). New gravity models with explicit links between matter and geometry instead involve second-order derivatives of $\mathcal{L}_{m}$ relative to the metric tensor. So, picking either $p$ or $-ρ$ for $\mathcal{L}_{m}$ gives different effective EFEs. This confusion appears because one usually treats the four-velocity ($u_μ$) and the metric tensor ($g_{μν}$) as independent. Here, we revisit the basics and offer a consistent framework by relaxing that assumption, thereby making the modified gravity theory independent of the choice of $\mathcal{L}_{m}$. Finally, we test this approach on neutron and quark stars (ultraviolet region) and on cosmological situations with radiation-dominated ($p=ρ/3$) equations of state (infrared region), showing how it clarifies the ambiguity in picking $\mathcal{L}_{m}$ for gravity models.
Comments30 pages, 4 figures, under reviewed in European Physical Journal C
