具有正负质量的引力Vlasov-Poisson系统中的致密核-壳平衡态
Compact Core--Shell Equilibria in Gravitational Vlasov--Poisson Systems with Positive and Negative Mass
浏览论文内容
中文总结 AI 辅助
该研究在恒星动力学中构建了正负质量引力Vlasov-Poisson系统的致密核-壳平衡态，分析两种负质量约定下的稳态结构，为负质量分布研究提供动力学框架。
中文摘要 AI 辅助
我们在恒星动力学背景下，构建了由正负质量分布源产生的引力Vlasov-Poisson系统的正则、球对称、致密能量截断平衡态。受Bondi负质量概念及其与带符号质能源的爱因斯坦引力弱场极限关系的启发，我们证明了稳态的内部结构在定性上取决于所存在的负质量类型。在Bondi约定下，惯性质量、被动引力质量和主动引力质量的符号同时反转，保持等效原理不变。由此产生的平衡态包含一个同时存在两种质量的中心重叠核，周围环绕着有限的正质量壳和外部真空。因此，尽管纯Bondi负质量气体无法形成致密稳态，但Bondi负质量可通过合适的正质量分布在空间上被约束。在引力荷约定下，仅被动和主动引力质量改变符号，使得两种物质遵循相反的自由下落定律，且不同质量相互排斥。由此产生的平衡态在空间上分离为负质量核、真空间隙、正质量壳和外部真空。对于截断指数n=-1/2，径向匹配是显式的；而对于正则截断n=1/2，物质区域满足Lane-Emden型方程。这些结果为研究天体物理和宇宙学环境中负质量的分布提供了动力学框架。
英文摘要
We construct regular, spherically symmetric, compact energy-cutoff equilibria for gravitational Vlasov--Poisson systems sourced by positive and negative mass distributions in the context of stellar dynamics. Motivated by Bondi's notion of negative mass and its relation to the weak field limit of Einstein gravity with a signed mass--energy source, we show that the internal structure of the steady states depends qualitatively on the type of negative mass present. In the Bondi convention, the signs of inertial, passive gravitational, and active gravitational mass are reversed together, preserving the equivalence principle. The resulting equilibria consist of a central overlap core containing both mass species, surrounded by a finite positive mass shell and an exterior vacuum. Thus, although a pure Bondi negative mass gas cannot form a compact steady state, Bondi negative mass can be spatially confined by a suitable positive mass distribution. In the gravitational-charge convention, only the passive and active gravitational masses change sign, so that the two species obey opposite free-fall laws and unlike masses repel. The resulting equilibria are spatially segregated into a negative mass core, a vacuum gap, a positive mass shell, and an exterior vacuum. For cutoff exponent $n=-1/2$, the radial matching is explicit, while for the regular cutoff $n=1/2$ the matter regions satisfy Lane--Emden-type equations. These results provide a kinetic framework for investigating the distribution of negative mass in astrophysical and cosmological settings.
