标题： 自引力场构型：能量-动量迹的作用 显示英文标题

标题： Self-gravitating field configurations: The role of the energy-momentum trace

摘要： 研究了广义相对论框架下能量-动量张量具有非负迹的静态球对称物质分布。 我们证明，这种场构型必然是高度相对论性的物体。 特别是，对于满足 $T\geq\alpha\cdot\rho\geq0$ （这里 $T$和 $\rho$分别是能量-动量张量的迹和场的能量密度，而 $\alpha$是一个非负常数）的物质场，我们得到了正则场构型紧凑性（质量与半径比值）的一个下界 $\text{max}_r\{2m(r)/r\}>(2+2\alpha)/(3+2\alpha)$。 此外，我们证明这些紧凑物体必然至少拥有 {\it 两个} 个光子球，其中一个表现出 {\it 稳定} 的零测地线俘获。 相应弯曲时空中的稳定光子球的存在表明，这些紧凑物体可能是非线性不稳定的。 因此，我们推测能量-动量张量的负迹是广义相对论中稳定、类孤子（规则）场构型存在的{\it 必要的}条件。 显示英文摘要

摘要： Static spherically-symmetric matter distributions whose energy-momentum tensor is characterized by a non-negative trace are studied analytically within the framework of general relativity. We prove that such field configurations are necessarily highly relativistic objects. In particular, for matter fields with $T\geq\alpha\cdot\rho\geq0$ (here $T$ and $\rho$ are respectively the trace of the energy-momentum tensor and the energy density of the fields, and $\alpha$ is a non-negative constant), we obtain the lower bound $\text{max}_r\{2m(r)/r\}>(2+2\alpha)/(3+2\alpha)$ on the compactness (mass-to-radius ratio) of regular field configurations. In addition, we prove that these compact objects necessarily possess (at least) {\it two} photon-spheres, one of which exhibits {\it stable} trapping of null geodesics. The presence of stable photon-spheres in the corresponding curved spacetimes indicates that these compact objects may be nonlinearly unstable. We therefore conjecture that a negative trace of the energy-momentum tensor is a {\it necessary} condition for the existence of stable, soliton-like (regular) field configurations in general relativity.