English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Existence and uniqueness of rotating fluid bodies in equilibrium is stillpoorly understood in General Relativity (GR). Apart from the limiting case ofinfinitely thin disks, the only known global results in the stationary rotatingcase (Heilig [14] and Makino [21] [arXiv:1705.07392]) show existence in GRnearby a Newtonian configuration (under suitable additional restrictions). Inthis work we prove existence and uniqueness of rigidly (slowly) rotating fluidbodies in equilibrium to second order in perturbation theory in GR. The mostwidely used perturbation framework to describe slowly rigidly rotating stars inthe strong field regime is the Hartle-Thorne model. The model involves a numberof hypotheses, some explicit, like equatorial symmetry or that the perturbationparameter is proportional to the rotation, but some implicit, particularly onthe structure and regularity of the perturbation tensors and the conditions oftheir matching at the surface. In this work, with basis on the gauge resultsobtained in [25], the Hartle-Thorne model is fully derived from firstprinciples and only assuming that the perturbations describe a rigidly rotatingfinite perfect fluid ball (with no layer at the surface) with the samebarotropic equation of state as the static ball. Rigidly rotating fluid ballsare analyzed consistently in second order perturbation theory by imposing onlybasic differentiability requirements and boundedness. Our results prove inparticular that, at this level of approximation, the spacetime must be indeedequatorially symmetric and is fully determined by two parameters, namely thecentral pressure and the uniform angular velocity of the fluid.

Existence and uniqueness of compact rotating configurations in GR in second order perturbation theory