In this paper, we find a four-dimensional metric for a large black hole immersed in dark matter. Specifically, we look for and find a static spherically symmetric black hole solution to the Einstein equations which gives, in the Newtonian limit, the rotation curves of galaxies, including the flat region and the baryonic Tully–Fisher relation, and which has a regular horizon. We obtain as well the energy–momentum tensor of the dark matter sourcing this spacetime and it turns, in special, to satisfy the four energy conditions (dominant, weak, null and strong) everywhere outside the horizon. This black-hole-dark-matter system represents a successful simplified model for galaxies, opens a new area for exploring the relativistic regime of dark matter, and shows that the theory of General Relativity together with dark matter can account for the rotation curves of galaxies.

中文翻译：

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暗物质内部的黑洞和星系的旋转曲线

在这篇论文中，我们找到了一个沉浸在暗物质中的大黑洞的四维度量。具体来说，我们寻找并找到爱因斯坦方程的静态球对称黑洞解，它在牛顿极限内给出了星系的旋转曲线，包括平坦区域和重子 Tully-Fisher 关系，并且具有规则的视界. 我们还获得了来自这个时空的暗物质的能量-动量张量，它特别地满足了视界外各处的四种能量条件（主导、弱、零和强）。这个黑洞-暗物质系统代表了一个成功的星系简化模型，为探索暗物质的相对论机制开辟了一个新领域，