Böhmer Christian G, Burikham Piyabut, Harko Tiberiu, Lake Matthew J
1Department of Mathematics, University College London, Gower Street, London, WC1E 6BT UK.
2High Energy Physics Theory Group, Department of Physics, Faculty of Science, Chulalongkorn University, Phyathai Rd, Bangkok, 10330 Thailand.
Eur Phys J C Part Fields. 2018;78(3):253. doi: 10.1140/epjc/s10052-018-5719-y. Epub 2018 Mar 23.
We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass-radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein-Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass.
我们推导了爱因斯坦 - 嘉当理论中自旋流体球体质量 - 半径比的上限和下限，其中物质满足线性正压状态方程，且存在宇宙学常数。采用球对称内部几何结构，我们得到了处于流体静力学平衡的魏森霍夫自旋流体的广义连续性方程和托尔曼 - 奥本海默 - 沃尔科夫方程，这些方程用有效质量、密度和压力表示，所有这些都包含来自自旋的额外贡献。得到了在内部任何一点都有效的广义布赫达赫尔不等式，并推导了最大和最小质量 - 半径比的一般理论极限。作为我们结果的一个应用，我们得到了致密自旋流体物体的引力红移界限，这在原则上可用于在天体物理背景下对爱因斯坦 - 嘉当理论的观测检验。我们还简要考虑了挠率诱导的最小质量在重子/介子的自旋广义强引力模型中的应用，并表明量子自旋的存在对自旋粒子施加了一个下限，该下限几乎精确地再现了电子质量。
