各向同性恒星种子统一族引力解耦的闭式主解
A Closed-Form Master Solution for Gravitational Decoupling of a Unified Family of Isotropic Stellar Seeds
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中文总结 AI 辅助
本文提出基于最小几何形变的统一闭式主解，将五类各向同性种子解推广为各向异性致密星，并分析其物理可行性及潮汐形变增强效应。
中文摘要 AI 辅助
我们提出了一种基于最小几何形变（MGD）的各向异性致密星统一方案，该方案建立在一个双参数种子族 $\nu(r)=\text{Ln}[C(1+ar^{2n})^{m}]$ 之上，其径向度规势 $\mu(r)=e^{-\lambda(r)}$ 由各向同性条件以闭式确定。在 $n=1$ 时，该族分别以 $m=1,2,3,4,5$ 的特殊情形重现 Tolman IV、Korkina--Orlyanskii、Heintzmann IIa 和 Durgapal IV--V 解。关键结果是，通过一个源函数 $g(r)$ 实现了 MGD $\theta$-扇区的单一闭合，该函数以 Gauss 超几何函数 ${}_2F_1$ 的形式，对 \u003cem\u003e任意\u003c/em\u003e $(n,m)$ 将解耦方程以闭式积分：因此，$n=1$ 族的各向异性推广可由一个主公式获得。我们推导了有效的各向异性物质含量、与外部 Schwarzschild 真空的 Darmois--Israel 匹配，以及约束参数空间的全部物理可接受性判据，并针对 $n=1$ 情形显式绘制了致密度和解耦强度中的允许区域：Tolman IV 和 Korkina--Orlyanskii 在任意高致密度下均允许物理上一致的各向异性形变，而 Heintzmann IIa 和 Durgapal IV--V 则受致密度上限约束，超过该上限后任何解耦参数值都无法恢复因果性。利用相同的闭式物质含量，我们计算了允许区域内的四极潮汐 Love 数和无量纲潮汐形变率，发现相对于固定致密度下的各向同性种子，解耦系统地增强了这两者，且在 Heintzmann 和 Durgapal 分支中接近因果上限时出现急剧上升。
英文摘要
We present a unification scheme for anisotropic compact stars generated via minimal geometric deformation (MGD), built on a two-parameter seed family $ν(r)=\text{Ln}[C(1+ar^{2n})^{m}]$ whose radial metric potential $μ(r)=e^{-λ(r)}$ is fixed in closed form by the isotropy condition. At $n=1$ the family reproduces Tolman IV, Korkina--Orlyanskii, Heintzmann IIa, and Durgapal IV--V as the particular cases $m=1,2,3,4,5$. The key result is a single closure of the MGD $θ$-sector, through one source function $g(r)$, that integrates the decoupler equation in closed form, in terms of the Gauss hypergeometric function ${}_2F_1$, for \emph{arbitrary} $(n,m)$: the anisotropic extension of the $n=1$ family is thus obtained from one master formula. We derive the effective anisotropic matter content, the Darmois--Israel matching to the exterior Schwarzschild vacuum, and the full set of physical acceptability criteria constraining the parameter space, and map the admissible region in compactness and decoupling strength explicitly for the case $n=1$: Tolman IV and Korkina--Orlyanskii admit physically consistent anisotropic deformations at arbitrarily high compactness, while Heintzmann IIa and Durgapal IV--V are bounded by a compactness ceiling beyond which no value of the decoupling parameter restores causality. Using the same closed-form matter content, we compute the quadrupolar tidal Love number and dimensionless tidal deformability across the admissible region, finding that the decoupling systematically enhances both relative to the isotropic seed at fixed compactness, with a sharp rise near the causal ceiling in the Heintzmann and Durgapal branches.
发表机构
- GLA University（GLA大学）
- King Faisal University（费萨尔国王大学）
- Teerthanker Mahaveer University（特兰坎克尔·马哈维尔大学）
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