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timmdeeg

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The Importance of Being Symmetric: Flat Rotation Curves from Exact Axisymmetric Static Vacuum Spacetimes

Antonia Seifert is a master's student of Prof. Bartelmann, Heidelberg.

*... Analyzing the low-velocity limitcorresponding to the Newtonian approximation of the Schwarzschild metric, we find an effective logarithmic potential. Thisyields flat rotation curves for test particles undergoing rotational motion within the spacetime described by the line elements,in contrast to Newtonian rotation curves. This analysis highlights how important the symmetry assumptions are for deriving general relativistic solutions.*

One example of physical objects that are generally described in the static vacuum low-velocity limit (reducing to Newtonian gravity in the spherically symmetric case) and exhibit axial symmetry are disk galaxies. We show that symmetries and appropriate line elements that respect them are crucial to consider in such settings. In particular, the solutions presented here result in flatrotation curves without any need for dark matter. While these exact solutions are limited to static vacuum spacetimes, their application to physical galaxies relies on appropriate approximations. Nonetheless, they offer valuable insights into explanations for flat rotation curves in galaxies and their implications for dark matter.One example of physical objects that are generally described in the static vacuum low-velocity limit (reducing to Newtonian gravity in the spherically symmetric case) and exhibit axial symmetry are disk galaxies. We show that symmetries and appropriate line elements that respect them are crucial to consider in such settings. In particular, the solutions presented here result in flatrotation curves without any need for dark matter. While these exact solutions are limited to static vacuum spacetimes, their application to physical galaxies relies on appropriate approximations. Nonetheless, they offer valuable insights into explanations for flat rotation curves in galaxies and their implications for dark matter.

Antonia Seifert is a master's student of Prof. Bartelmann, Heidelberg.

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