圈量子引力中有效聚合物几何描述的白矮星恒星结构
White Dwarf Stellar Structure from Effective Polymer Geometry in Loop Quantum Gravity
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中文总结 AI 辅助
该研究基于圈量子引力的聚合物几何构建白矮星有效TOV系统，发现参数Aλ可使白矮星最大质量超钱德拉塞卡极限，η影响极小。
中文摘要 AI 辅助
我们基于圈量子引力（Loop Quantum Gravity）提出的聚合物度规部分的面积半径形式，构建了冷碳白矮星的有效托尔曼-奥本海默-沃尔科夫（Tolman Oppenheimer Volkoff）系统。几何的两个渐近质量参数通过 $M_B\rightarrow m(R)$ 和 $M_W=\eta m(R)$ 保留在恒星模型中，而聚合物振幅由 $A_\lambda$ 控制。物质部分保持固定，采用钱德拉塞卡（Chandrasekhar）物态方程及带有库仑晶格修正的相同碳模型。所得方程可恢复广义相对论的TOV系统和对称聚合物极限。对于未变形序列，钱德拉塞卡模型的最大质量 $M_{\max}=1.4166\\,M_\odot$，包含晶格修正时为 $1.3850\\,M_\odot$。开启 $A_\lambda$ 后，平衡序列的大质量部分向上偏移，且未使物态方程变硬，当 $A_\lambda=100$ 时，两种物质模型的最大质量分别达到 $1.7125\\,M_\odot$ 和 $1.6907\\,M_\odot$，这些构型仍处于扫描所用逆β衰变边界限定的物质域内。非对称比 $\eta=M_W/M_B$ 会改变聚合物跃迁区域附近的度规函数，但对白矮星观测量的影响很小：在所选构型中，$M_{\max}$ 变化小于0.1%，对应半径变化小于0.33%。因此，该计算确定 $A_\lambda$ 是控制质量-半径关系超钱德拉塞卡位移的参数，而 $\eta$ 主要作为白矮星探测的低致密性区域的几何非对称参数。
英文摘要
We construct an effective Tolman Oppenheimer Volkoff system for cold carbon white dwarfs using the areal radius form of a polymer metric sector motivated by loop quantum gravity. The two asymptotic mass parameters of the geometry are retained in the stellar prescription through $M_B\rightarrow m(R)$ and $M_W=ηm(R)$, while the polymer amplitude is controlled by $A_λ$. The matter sector is kept fixed and is described by the Chandrasekhar equation of state and by the same carbon model with the Coulomb lattice correction. The resulting equations recover the general relativistic TOV system and the symmetric polymer limit. For the undeformed sequences we obtain $M_{\max}=1.4166\,M_\odot$ for the Chandrasekhar model and $M_{\max}=1.3850\,M_\odot$ when the lattice correction is included. Turning on $A_λ$ shifts the massive part of the equilibrium sequence upward without stiffening the equation of state, reaching $M_{\max}=1.7125\,M_\odot$ and $1.6907\,M_\odot$ at $A_λ=100$ for the two matter models. These configurations remain within the matter domain imposed by the inverse beta decay boundary used in the scan. The asymmetric ratio $η=M_W/M_B$ changes the metric function near the polymer transition region, but its effect on white dwarf observables is small: across the selected configurations, $M_{\max}$ changes by less than $0.1\%$ and the corresponding radius by less than $0.33\%$. The calculation therefore identifies $A_λ$ as the parameter controlling the super Chandrasekhar displacement of the mass radius relation, while $η$ acts mainly as a geometric asymmetry parameter in the low compactness regime probed by white dwarfs.
