The flat limit of rotational velocity (v<sub>φ</sub>) approximately equal to the “edge”-velocity of a galaxy is related to the baryonic mass (M<sub>B</sub>) via the T-F relationship w...The flat limit of rotational velocity (v<sub>φ</sub>) approximately equal to the “edge”-velocity of a galaxy is related to the baryonic mass (M<sub>B</sub>) via the T-F relationship with n ≈ 4. We explore the connection between mass and the limiting velocity in the framework of general relativity (GR) using the Weyl metric for axially-symmetric galaxies that are supported entirely by their rotational motion. While for small distances from the center, the Newtonian description is accurate as one moves beyond the (baryonic) edge of the galaxy, Lenz’s law and non-linearity of the gravitational field inherent in GR not only lead to a flat velocity (obviating its Keplerian fall), but also provide its tight log-log relationship with the enclosed (baryonic) mass.展开更多
Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded an...Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded and the ungraded strongly Gorenstein modules.展开更多
文摘The flat limit of rotational velocity (v<sub>φ</sub>) approximately equal to the “edge”-velocity of a galaxy is related to the baryonic mass (M<sub>B</sub>) via the T-F relationship with n ≈ 4. We explore the connection between mass and the limiting velocity in the framework of general relativity (GR) using the Weyl metric for axially-symmetric galaxies that are supported entirely by their rotational motion. While for small distances from the center, the Newtonian description is accurate as one moves beyond the (baryonic) edge of the galaxy, Lenz’s law and non-linearity of the gravitational field inherent in GR not only lead to a flat velocity (obviating its Keplerian fall), but also provide its tight log-log relationship with the enclosed (baryonic) mass.
基金Acknowledgements This work was Foundation of China （Grant No. 11371187） Province of China （Grant No. BK20160771） supported by the National Natural Science and the Natural Science Foundation of Jiangsu
文摘Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded and the ungraded strongly Gorenstein modules.
