极端$\ell$ -玻色子星
Extreme $\ell$-boson stars
摘要：
最近发现了一类新的复标量场对象，它推广了著名的玻色子星，作为Einstein-Klein-Gordon系统的解。一般化包括纳入角动量的一些影响，同时仍然保持时空的球对称性。这些新的解依赖于一个（整数）角参数$\ell$，因此被命名为$\ell$玻色子星。像标准的$\ell=0$玻色子星一样，这些配置在解空间中有一个稳定的分支;然而，与它们相反，它们的形态呈现出壳状结构，内部区域有一个“洞”。在这篇文章中，我们进行了彻底的探索的参数空间，特别是集中在极端情况下，大值的$\ell$。我们表明，壳的大小与角参数，这样做的线性大值，与大小增长速度比厚度。它们的质量也随着$\ell$的增加而增加，但是以这样一种方式，它们的紧凑性，同时也单调增长，收敛到一个有限的值，对应于稳定构型的布赫达尔极限的一半左右。此外，我们表明，$\ell$玻色子星可以是高度各向异性的，与径向压力减少相对于大$\ell$的切向压力，渐近减少到零，最大密度也接近零。通过分析场方程及其解的渐近极限$\ell\rightarrow\infty$，我们证明了这些性质可以得到理解。我们还分析了类时和零圆轨道的存在性和特征，特别是对于非常紧的解。
英文摘要：
A new class of complex scalar field objects, which generalize the well known boson stars, was recently found as solutions to the Einstein-Klein-Gordon system. The generalization consists in incorporating some of the effects of angular momentum, while still maintaining the spacetime's spherical symmetry. These new solutions depend on an (integer) angular parameter $\ell$, and hence were named $\ell$-boson stars. Like the standard $\ell=0$ boson stars these configurations admit a stable branch in the solution space; however, contrary to them they have a morphology that presents a shell-like structure with a "hole" in the internal region. In this article we perform a thorough exploration of the parameter space, concentrating particularly on the extreme cases with large values of $\ell$. We show that the shells grow in size with the angular parameter, doing so linearly for large values, with the size growing faster than the thickness. Their mass also increases with $\ell$, but in such a way that their compactness, while also growing monotonically, converges to a finite value corresponding to about one half of the Buchdahl limit for stable configurations. Furthermore, we show that $\ell$-boson stars can be highly anisotropic, with the radial pressure diminishing relative to the tangential pressure for large $\ell$, reducing asymptotically to zero, and with the maximum density also approaching zero. We show that these properties can be understood by analyzing the asymptotic limit $\ell\rightarrow\infty$ of the field equations and their solutions. We also analyze the existence and characteristics of both timelike and null circular orbits, especially for very compact solutions.
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