Lovelock引力中的静态各向异性恒星：通用闭式方程
Static anisotropic stars in Lovelock gravity: Universal closed-form equations
AI总结：
该研究将Lovelock引力中静态理想流体的特征多项式公式扩展至各向异性物质领域，推导了相关闭式方程，证实内部Schwarzschild几何的唯一性，消除d=2N+1维纯Lovelock球的障碍，并积分得到d=10、11维的恒星方程，发现高阶项可增大最大质量。
AI中文摘要：
针对Lovelock引力中的静态理想流体，已有特征多项式公式[Phys. Rev. D 113, 084008 (2026)]，我们将其扩展至完整的各向异性物质领域。对于任意维度及独立耦合的曲率阶数，我们推导了密度、径向压强、切向压强与各向异性的无求和闭式表达式，这些表达式以单个多项式\boldsymbol{W}、其导数及两个派生多项式\boldsymbol{V}、\boldsymbol{U}表示。依赖于维度的组合系数可直接由广义δ反对称化得到，并通过归纳法独立验证。施加压强各向同性条件可得到已知的全导数方程，我们将其分解为对Lovelock阶数为仿射、对维度为线性的显式算子。该结构证明，除角截面曲率为零的分支外，内部Schwarzschild几何是任意Lovelock耦合共有的唯一各向同性内部几何；还将d=2N+1维中有界纯Lovelock球的固定符号障碍与多项式恒等式\boldsymbol{V}\boldsymbol{\bar{=}}\boldsymbol{0}关联，显示低阶项或宇宙学项可消除该障碍。最后，我们对d=10和d=11维中所有允许阶数均激活的任意阶恒星方程进行积分，对于所考虑的正单参数Lovelock耦合层级，广义相对论序列拓扑保持不变，而高阶项会累积性地增大最大质量。
英文摘要：
A characteristic-polynomial formulation is already known for static perfect fluids in Lovelock gravity [Phys. Rev. D 113, 084008 (2026)]. We extend it to the complete anisotropic matter sector. For arbitrary dimension and independently coupled curvature orders, we derive closed, summation-free expressions for the density, radial pressure, tangential pressure and anisotropy in terms of a single polynomial \(W\), its derivatives and two derived polynomials \(V\) and \(U\). The dimension-dependent combinatorial coefficients are obtained directly from the generalized-delta antisymmetrisation and independently confirmed through an inductive argument. Imposing pressure isotropy recovers the known total-derivative equation, which we resolve into an explicit operator affine in Lovelock order and linear in dimension. This structure proves that, apart from the branch of vanishing angular sectional curvature, the interior Schwarzschild geometry is the unique isotropic interior common to arbitrary Lovelock couplings. It also identifies the fixed-sign obstruction to bounded pure Lovelock spheres in \(d=2N+1\) with the polynomial identity \(V\equiv0\), and shows how a lower-order term or cosmological term removes this obstruction. Finally, we integrate the resulting arbitrary-order stellar equations with all admissible orders active in \(d=10\) and \(d=11\). For the positive single-parameter hierarchy of Lovelock couplings considered, the general-relativistic sequence topology persists while higher orders increase the maximum mass cumulatively.
