Rapidly Rotating Stars

Yilun Wu; Walter Strauss

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arXiv · 1804.05413

Rapidly Rotating Stars

Yilun Wu·Walter Strauss

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Abstract

A rotating star may be modeled as a continuous system of particles attracted to each other by gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler-Poisson system. We prove an existence theorem for such stars that are rapidly rotating, depending continuously on the speed of rotation. This solves a problem that has been open since Lichtenstein's work in 1933. The key tool is global continuation theory, combined with a delicate limiting process. The solutions form a connected set $\mathcal K$ in an appropriate function space. As the speed of rotation increases, we prove that {\it either the supports of the stars in $\mathcal K$ become unbounded or the density somewhere within the stars becomes unbounded}. We permit any equation of state of the form $p=ρ^γ,\ 6/5<γ<2$, so long as $γ\ne4/3$. We consider two formulations, one where the angular velocity is prescribed and the other where the angular momentum per unit mass is prescribed.

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Yilun Wu, Walter Strauss. 2018-04-15. Rapidly Rotating Stars. https://arxiv.org/abs/1804.05413

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