发表机构
University of KwaZulu-Natal; University College London（夸祖鲁-纳塔尔大学; 伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究基于BJ提出的体-边界分解引力理论，在纯二次体项情况下，通过假设势的比例关系构造出符合物理要求的各向同性流体壳，其等温流体行为与爱因斯坦模型相当。
AI 中文摘要
Böhmer和Jensko（简称BJ）提出，将里奇标量分解为体项和边界项可构建一种有趣的引力场理论，BJ进而给出了拉格朗日量中体项的函数形式。在天体物理建模中，边界项是非动力学的，整个理论仅由体项构建。针对共形静态度规背景，推导了恒星理想流体分布的场方程。由于体项函数的线性形式等价于爱因斯坦引力，本文研究复杂度更高的纯二次情况，其场方程远比爱因斯坦方程复杂。即使选择其中一个几何势函数为简单形式，压力各向同性方程也难以处理，因此分析势随半径反比变化的情况，但该情况无法得到可行模型，故假设势之间存在比例关系，结果可构建出满足基本物理要求的物理合理的各向同性流体壳。最后研究等温流体，其密度和压力均随半径的平方反比变化，得到的流体行为与对应爱因斯坦模型中的流体行为相当。
英文摘要
The decomposition of the Ricci scalar in terms of bulk and boundary terms gives rise to an interesting gravitational field theory as proposed by Böhmer and Jensko (BJ). BJ went on to suggest functional forms of the bulk contributions in the Lagrangian. For the purposes of astrophysical modelling the boundary terms are non-dynamical and the entire theory is built from the bulk contribution only. The field equations for a stellar perfect fluid distribution are obtained against the background of a conformostatic metric. Since the linear form of the function of the bulk term is equivalent to Einstein we probe the next level of complexity namely the pure quadratic case. The field equations are substantially more complicated than Einstein's equations. The equation of pressure isotropy proves intractable even with simple choices of one of the geometric potential functions. Accordingly we analyse the case of the potentials varying inversely with the radius. Viable models do not arise in this case and so we postulate a proportional relationship between the potentials. It turns out that a physically reasonable shell of isotropic fluid may be constructed that satisfies elementary physical requirements. Finally we investigate the isothermal fluid where both density and pressure go as the inverse square law of the radius. This results in fluid behaviour that is comparable to that in the corresponding Einstein model.
Comments20 pages, 3 figures
Journal refPhysics Letters B880 (2026) 140764
DOI：10.1016/j.physletb.2026.140764
