A static structure of matter, extremely compressed to the state of a Bose–Einstein condensate by its own gravitational field, is considered. Instead of the widely spread restriction $det{g}_{ik}<0$, I used a weaker condition of regularity: all invariants of $g_{ik}$ are finite. This makes it possible to find regular static solutions to Einstein equations for a spherically symmetric distribution of matter with no restriction on total mass. In these regular static solutions, the metric component $g^{rr}$ changes its sign twice: $g^{rr}\left(r\right)=0$ at $r=r_g$ and at $r=r_h>r_g$. The signature of the metric tensor is changed to (+,+,−,−) within the spherical layer $r_g<r<r_h$. Though the gravitation dominates at extremely high density, I assume that it does not violate the exchange interaction of elementary particles of the Standard Model. The found regular static solution to Einstein equations, having no limitation on mass, pretends to describe the state of a black hole to which the gravitational collapse leads. The features of a collapsed black hole, its internal composition depending on total mass and the relation with surrounding dark matter, are considered. An astrophysical application: The pressure balance at the interface between a black hole and dark matter determines the plateau velocity of a galaxy rotation curve as a function of the black hole mass. The plateau velocity is inversely proportional to the black hole mass. The speed of rotation of a star at the periphery of a galaxy is proportional to the square root of the black hole mass (direct attraction to the center) and inversely proportional to the mass of the same black hole (as the influence of dark matter). For a condensate of massive bosons in the Standard Model, the direct attraction to the black hole and the influence of dark matter are equal if the black hole mass is about $\tilde{M}$∼$4.24\times {10}^{37}$ g. In galaxies with black hole masses $M\gtrsim M_{\odot }=1.989\times {10}^{33}$ g (like UMa: NGC 3726 and UMa: NGC 3769 of the Ursa Major cluster), the motion of stars is driven by dark matter. Their rotation curves should have a well-defined plateau. On the contrary, in galaxies with black hole masses $M>>\tilde{M}$ (like in our Milky Way with the black hole mass $M=8.6\times {10}^{39}$ g), the motion of stars is regulated by the black hole in the center. Dark matter does not play a significant role in our Milky Way Galaxy.

中文翻译：

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黑洞之谜：猜一个黑洞之谜

考虑了一种静态的物质结构，该结构由其自身的引力场极大地压缩为玻色-爱因斯坦凝聚物的状态。代替广泛传播的限制$det{G}_{\mathrm{一世}ķ}<0$，我使用了较弱的规律性条件： $G_{\mathrm{一世}ķ}$是有限的。这使得可以为物质的球对称分布找到对爱因斯坦方程的正则静态解，而对总质量没有限制。在这些常规静态解决方案中，指标组件$G^{\mathrm{[R}\mathrm{[R}}$ 两次更改其符号： $G^{\mathrm{[R}\mathrm{[R}}（\mathrm{[R}）=0$ 在 $\mathrm{[R}={\mathrm{[R}}_G$ 在 $\mathrm{[R}={\mathrm{[R}}_H>{\mathrm{[R}}_G$。在球形层中，度量张量的签名更改为（+，+，-，-）${\mathrm{[R}}_G<\mathrm{[R}<{\mathrm{[R}}_H$。尽管重力以极高的密度占主导地位，但我认为它不违反标准模型的基本粒子的交换相互作用。对质量没有限制的，对爱因斯坦方程式找到的正则静态解伪装成描述了引力坍塌导致的黑洞的状态。考虑了塌陷的黑洞的特征，其内部成分取决于总质量以及与周围暗物质的关系。天文学的应用：黑洞与暗物质之间的界面处的压力平衡决定了星系旋转曲线的平稳速度，该速度是黑洞质量的函数。平稳速度与黑洞质量成反比。星系外围恒星的旋转速度与黑洞质量的平方根成正比（直​​接吸引到中心），与同一个黑洞质量的平方成反比（受暗物质的影响） 。对于标准模型中的大量玻色子的冷凝物，如果黑洞质量约为，则对黑洞的直接吸引和暗物质的影响是相等的$\stackrel{〜}{\mathrm{中号}}$〜$4。24\times {10}^{37}$G。在黑洞质量的星系中$\mathrm{中号}\gtrsim {\mathrm{中号}}_{\odot }=\mathrm{1个}。989\times {10}^{33}$g（类似于Ursa Major星团的UMa：NGC 3726和UMa：NGC 3769），恒星的运动是由暗物质驱动的。它们的旋转曲线应具有明确的平台。相反，在具有黑洞质量的星系中$\mathrm{中号}>>\stackrel{〜}{\mathrm{中号}}$ （例如在我们的银河系中有黑洞团 $\mathrm{中号}=8。6\times {10}^{39}$g），恒星的运动受中心黑洞的调节。暗物质在我们的银河系中没有扮演重要角色。