非线性sigma模型下的玻色子星
Boson stars with nonlinear sigma models
AI总结：
本文研究非线性sigma模型对玻色子星的影响，发现动能项曲率显著改变星体性质：O(3)星致密，SL(2,ℝ)星弥散，表明动能项与势同等重要。
摘要：
玻色子星作为与引力耦合的大质量复标量场的解而出现。文献中已经研究了多种标量势，它们产生了不同类型的玻色子星。这里我们转而研究将标量场的动能项提升为非线性sigma模型的影响——这一扩展自然受到弦理论等引力UV完备化的启发。我们考虑具有最小相互作用势的O(3)和SL(2,ℝ) sigma模型，并得到它们的玻色子星解。我们研究了解的最大质量和致密性作为sigma模型曲率的函数，并将结果与迷你玻色子星的典型情况进行了比较，后者在曲率消失时恢复。曲率的影响被证明是巨大的。虽然O(3)星质量大且可以达到R~3.3 GM的致密尺寸，但SL(2,ℝ)星则弥散得多，并且只有在玻色子为超轻时在天体物理上才可行。这些结果表明，标量动能项在决定玻色子星性质方面至少与势同样重要。
英文摘要：
Boson stars arise as solutions of a massive complex scalar field coupled to gravity. A variety of scalar potentials, giving rise to different types of boson stars, have been studied in the literature. Here we study instead the effect of promoting the kinetic term of the scalar field to a nonlinear sigma model -- an extension that is naturally motivated by UV completions of gravity like string theory. We consider the $\mathrm{O}(3)$ and $\mathrm{SL}(2,\mathbb{R})$ sigma models with minimally interacting potentials and obtain their boson star solutions. We study the maximum mass and compactness of the solutions as a function of the curvature of the sigma model and compare the results to the prototypical case of mini boson stars, which are recovered in the case of vanishing curvature. The effect of the curvature turns out to be dramatic. While $\mathrm{O}(3)$ stars are massive and can reach a size as compact as $R\sim 3.3 GM$, $\mathrm{SL}(2,\mathbb{R})$ stars are much more diffuse and only astrophysically viable if the bosons are ultralight. These results show that the scalar kinetic term is at least as important as the potential in determining the properties of boson stars.
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