Working in static spherically symmetric setup, recent study has demonstrated that the effective spacetime geometry of a Bose-Einstein condensate of weakly interacting gravitons is analogous to a gravastar, hence providing a bridge between these two attempts in describing the black hole interior. In this paper we make three generalizations: introducing a composite of two graviton condensates so that the exterior spacetime is not necessarily asymptotically flat, working in $f({\mathcal R})$ gravity, and extending the calculations to higher dimensions. We find that the effective spacetime geometry is again analogous to a gravastar, but the interior can be de Sitter or Anti-de Sitter and the exterior can be Schwarzschild, Schwarzschild-de Sitter, or Schwarzschild-Anti de Sitter, where the cosmological constant for the exterior must be smaller than the one for the interior. These geometries are determined by the modified gravity function $f({\mathcal R})$, in contrast to previous works where they were selected by hand. We also presented a new possible value for the size of the interior condensate provided a certain restriction is satisfied, which would not be met if we are still working in ordinary gravity with four spacetime dimensions. This restriction can be seen manifested in the behavior of the interior graviton wavelength as a function of spacetime dimension.

中文翻译：

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f(R) 引力中引力子凝聚的有效时空几何

在静态球对称设置中工作，最近的研究表明，弱相互作用引力子的玻色-爱因斯坦凝聚的有效时空几何类似于引力星，因此在描述黑洞内部的这两种尝试之间提供了一座桥梁。在本文中，我们进行了三个概括：引入两个引力子凝聚体的复合物，以便外部时空不一定是渐近平坦的，在 $f({\mathcal R})$ 引力下工作，并将计算扩展到更高的维度。我们发现有效时空几何再次类似于gravastar，但内部可以是de Sitter或Anti-de Sitter，外部可以是Schwarzschild、Schwarzschild-de Sitter或Schwarzschild-Anti de Sitter，其中外部的宇宙常数必须小于内部的宇宙常数。这些几何图形由修改后的重力函数 $f({\mathcal R})$ 确定，与以前手工选择的作品形成鲜明对比。我们还提出了一个新的内部冷凝物尺寸的可能值，前提是满足一定的限制，如果我们仍然在具有四个时空维度的普通重力下工作，则不会满足该限制。这种限制可以从作为时空维度函数的内部引力子波长的行为中看出。我们还提出了一个新的内部冷凝物尺寸的可能值，前提是满足一定的限制，如果我们仍然在具有四个时空维度的普通重力下工作，则不会满足该限制。这种限制可以从作为时空维度函数的内部引力子波长的行为中看出。我们还提出了一个新的内部冷凝物尺寸的可能值，前提是满足一定的限制，如果我们仍然在具有四个时空维度的普通重力下工作，则不会满足该限制。这种限制可以从作为时空维度函数的内部引力子波长的行为中看出。