理想流体能量-动量张量的度规变分及其在宇宙学和中子星中的应用
Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars
- Institute of physics, Vietnam academy of science
- technology (VAST), 10 Dao Tan, Hanoi, Viet Nam. addr1 Graduate university of science
- technology, Vietnam academy of science
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过直接计算标准能量-动量张量，推导出与物质拉格朗日量无关的度规变分表达式，并证明任意f(R,T)引力在标准宇宙组分下满足守恒律，构建的模型同时缓解哈勃张力并再现中子星质量-半径关系。
AI中文摘要：
我们证明，先前研究中得到的物质拉格朗日量 \\(L_m\\) 和理想流体的度规变分 \\(\delta T_{\mu\nu}\\) 的表达式在一般条件下与标准能量-动量张量不一致。因此，大量依赖这些表达式的天体物理学和宇宙学研究可能需要重新审视。通过直接对标准能量-动量张量 \\(T_{\mu\nu}\\) 并结合粒子数守恒条件进行一系列直接计算，我们推导出与 \\(L_m\\) 选择无关的 \\(\delta T_{\mu\nu}\\) 表达式。将此结果应用于 \\(f(R,T)\\) 引力，我们得到了张量 \\(\Theta_{\mu\nu} = g^{\sigma\rho} \frac{\delta T_{\sigma\rho}}{\delta g^{\mu\nu}}\\) 的精确形式，该量一直是一个重要但长期存在争议的量。该表达式也被证明适用于辐射，无论粒子数是否守恒。一个主要结果是：如果宇宙的能量-动量张量 \\(T_{\mu\nu}\\) 仅由标准组分（重子物质/冷暗物质、辐射和宇宙常数）组成，那么对于任意函数 \\(f(R,T)\\)，\\(f(R,T)\\) 引力都满足守恒律 \\(\nabla_\mu T^{\mu\nu} = 0\\)。这与先前的研究形成对比，先前研究发现守恒律仅对受限的 \\(f(R,T)\\) 函数类成立。将同样的形式体系应用于恒星内部，我们推导出一类保持守恒律的函数。我们构建了一个特定的 \\(f(R,T)\\) 模型，该模型在宇宙学尺度和中子星等高密度天体中都一致。值得注意的是，该模型中相同的参数组同时缓解了哈勃张力并再现了观测到的中子星质量-半径（M--R）关系。
英文摘要：
We show that the expressions for the matter Lagrangian \(L_m\) and the metric variation \(δT_{μν}\) of a perfect fluid obtained in previous studies appear to be inconsistent with the standard energy-momentum tensor under general conditions. Consequently, a large number of studies in astrophysics and cosmology relying on these expressions may need to be re-examined. By performing a series of straightforward calculations directly on the standard energy-momentum tensor \(T_{μν}\) together with the particle number conservation condition, we derive an expression for \(δT_{μν}\) that is independent of the choice of \(L_m\). Applying this result to \(f(R,T)\) gravity, we obtain the exact form of the tensor \(Θ_{μν} = g^{σρ} \frac{δT_{σρ}}{δg^{μν}}\), which remains an important yet long-standing controversial quantity. This expression is shown to hold also for radiation, regardless of whether particle number is conserved. A major result is that if the energy-momentum tensor \(T_{μν}\) of the Universe consists solely of standard components (baryonic/cold dark matter, radiation, and the cosmological constant), then \(f(R,T)\) gravity satisfies the conservation law \(\nabla_μT^{μν} = 0\) for any function \(f(R,T)\). This contrasts with previous studies, which found that the conservation law holds only for a restricted class of \(f(R,T)\) functions. Applying the same formalism to stellar interiors, we derive a class of functions that preserve the conservation law. We construct a specific \(f(R,T)\) model that is consistent at both cosmological scales and in high-density objects such as neutron stars. Remarkably, the same parameter set in this model simultaneously alleviates the Hubble tension and reproduces the observed mass-radius (M--R) relation of neutron stars.
