Structures in general relativity




Tieu, Steven

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Structures within general relativity are examined. The differences between man-made structures and those predicted by the Einstein differential equations are very subtle. Exotic structures such as the Godel Universe and the Gott cosmic string are examined with emphasis on closed time-like curves. Newtonian models are seen to also have an exotic aspect in that a vast halo consisting of unknown matter dominates the galaxy. We introduce a model for galaxies based on a general relativity framework with the goal of excluding such artifacts from the system while describing the flat-rotation curves. Structures within this model were speculated to be exotic but after close scrutiny, their nature is shown to be benign. Numerical approaches are applied to model four galaxies: The Milky Way, NGC 3031, NGC 3198 and NGC 7331. Density and mass are deduced from these models and compared to the Newtonian models. Within the visible/HI region, there is 30% reduction in total mass. Extending the model to 10 times beyond the HI region using various fall-off scenerios, it is shown that there is only modest increase of the accumulated mass. In comparison to the Newtonian approach to galactic dynamics, the massive halos are not required to account for the flat velocity profiles.



relativity (physics), galaxies