Nonstandard general relativity II
G\"unter Scharf
TL;DR
This paper explores solutions to Einstein's equations in a nonstandard gauge, enabling modeling of galactic bulges without dark matter by deriving spherically symmetric solutions from observed rotation curves.
Contribution
It introduces a novel approach to Einstein's equations in a nonstandard gauge for matter in hydrostatic equilibrium, extending previous vacuum solutions.
Findings
Derived spherically symmetric solutions for arbitrary rotation curves.
Demonstrated potential to model galactic bulges without dark matter.
Extended the nonstandard gauge analysis to matter-filled spacetimes.
Abstract
We study Einstein's equations with matter in hydrostatic equilibrium in the nonstandard gauge which was recently investigated in the vacuum case. We obtain spherically symmetric solutions for any given rotation curve. These solutions can be used to describe the bulge of a galaxy without assuming dark matter.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Philosophy and Theoretical Science · History and Theory of Mathematics