暗物质中的黑洞与银河系的转动曲线
A Black Hole inside Dark Matter and the Rotation Curves of Galaxies
摘要：
在这篇文章中，我们找到了一个四维度规的大黑洞沉浸在暗物质。具体地说，我们寻找并找到一个静态的球对称黑洞解的爱因斯坦方程，给出了，在牛顿极限，星系的旋转曲线，包括平坦的区域和重子Tully-Fisher关系，并有一个规则的视界。我们还得到了作为这个时空来源的暗物质的能量-动量张量，特别地，它在视界之外的任何地方都满足四个能量条件（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新的领域，并表明广义相对论理论和暗物质可以解释星系的自转曲线。
英文摘要：
In this article 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 space-time 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.
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