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 ℓ, and hence were named ℓ-boson stars. Like the standard ℓ = 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 ℓ. 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 ℓ, 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 ℓ-boson stars can be highly anisotropic, with the radial pressure diminishing relative to the tangential pressure for large ℓ, 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 ℓ → ∞ 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.

中文翻译：

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极端 ℓ-玻色子星

最近发现了一类新的复杂标量场对象，它概括了众所周知的玻色子星，作为爱因斯坦-克莱因-戈登系统的解决方案。概括包括结合一些角动量的影响，同时仍然保持时空的球对称性。这些新的解决方案取决于一个（整数）角度参数ℓ，因此被命名为ℓ-玻色子星。喜欢标准ℓ= 0 玻色子星这些配置在解空间中有一个稳定的分支；然而，与它们相反，它们的形态呈现出内部区域带有“孔”的壳状结构。在这篇文章中，我们对参数空间进行了彻底的探索，特别关注具有大值的极端情况ℓ. 我们表明壳的尺寸随着角度参数的增加而增加，对于大值呈线性增长，尺寸增长速度快于厚度。它们的质量也随着ℓ，但以这样一种方式，即它们的紧凑性，同时也单调增长，收敛到一个有限值，对应于稳定配置的 Buchdahl 极限的大约一半。此外，我们表明ℓ-玻色子星可以是高度各向异性的，径向压力相对于切向压力递减ℓ，逐渐减少到零，并且最大密度也接近零。我们表明可以通过分析渐近极限来理解这些属性ℓ→ ∞ 场方程及其解。我们还分析了类时和空圆轨道的存在和特征，特别是对于非常紧凑的解决方案。