零温度简并费米子星
Zero Temperature, Degenerate Fermion Stars
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中文总结 AI 辅助
本文提出一种自洽方法研究零温度简并费米子星，在牛顿极限下可构造比布赫达尔极限更致密甚至小于史瓦西半径的恒星，并在广义相对论半经典分析中独立恢复布赫达尔极限。
中文摘要 AI 辅助
我们研究一种静止质量为 $m$ 的简并、零温度费米子气体，该气体仅通过引力与自身相互作用。我们描述了一种自洽的新方法，用于形成简并的量子力学恒星。在这种方法中，费米子根据泡利不相容原理占据由自洽引力相互作用确定的能级。在这种新方法中，最高占据能级的大小决定了恒星的半径。在牛顿引力极限下，费米子感受到的势对应于一个简谐振子势阱，该势阱在外部平滑地连接到通常的 $1/r$ 牛顿引力势。我们解析地找到了具有任意半径和质量的恒星解，这些解由 $m$ 和 $N_s$（费米子总数）参数化。在牛顿极限下，我们很容易发现我们可以构造一颗比布赫达尔极限更致密的恒星，甚至确实可以小于史瓦西半径。显然，这种情况超出了牛顿极限的范围。因此，我们将分析扩展到广义相对论背景下的费米子，它们通过度规与引力相互作用。我们考虑对应于内部史瓦西解的度规，该解平滑地连接到通常的外部史瓦西度规。半经典地处理物质，我们在完全独立的分析中恢复了布赫达尔极限。我们简要讨论了牛顿解的经典稳定性及其与牛顿多方流体的关系。
英文摘要
We study a zero temperature, degenerate, fermion gas with fermions of rest mass $m$, that only interacts with itself, gravitationally. We describe a self-consistent novel approach to the formation of a degenerate, quantum mechanical, star. In this approach, the fermions occupy the energy levels that are determined by the self consistent gravitational interactions, according to the Pauli exclusion principle. Then the size of the highest occupied level determines the radius of the star. In the Newtonian gravitational limit, the fermions feel a potential corresponding to a simple harmonic well that smoothly attaches in the exterior to the usual $1/r$ Newtonian gravitational potential. We find analytically, solutions for stars with any radius and mass, parametrized by $m$ and $N_s$, the total number of fermions. In the Newtonian limit, we easily find that we can construct a star that is more compact than the Buchdahl bound and indeed can even be smaller than the Schwarzschild radius. Clearly, such cases are outside of the purview of the Newtonian limit. Therefore we expand our analysis to fermions in the general relativistic context, interacting gravitationally with a metric. We consider the metric corresponding to the interior Schwarzschild solution smoothly connecting to the usual exterior Schwarzschild metric. Treating matter semi-classically, we recover the Buchdahl bound in a completely independent analysis. We briefly discuss classical stability of the Newtonian solution, and its relation to Newtonian polytropic fluids.
发表机构
- Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）
- Université de Montréal（蒙特利尔大学）
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