Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium

TL;DR

This paper demonstrates that convective motions inside isolated rotating bodies in equilibrium do not affect their exterior gravitational fields, extending previous results to more general interior fluid motions in General Relativity.

Contribution

It generalizes the analysis of rotating bodies in equilibrium to include convective motions, proving they do not influence the exterior field and confirming the applicability of existing uniqueness and existence results.

Findings

Convective motions have no direct influence on the exterior gravitational field.

Existing uniqueness and existence results remain valid with general interior sources.

The study extends previous models by removing the circularity condition assumption.

Abstract

The problem of describing isolated rotating bodies in equilibrium in General Relativity has so far been treated under the assumption of the circularity condition in the interior of the body. For a fluid without energy flux, this condition implies that the fluid flow moves only along the angular direction, i.e. there is no convection. Using this simplification, some recent studies have provided us with uniqueness and existence results for asymptotically flat vacuum exterior fields given the interior sources. Here, the generalisation of the problem to include general sources is studied. It is proven that the convective motions have no direct influence on the exterior field, and hence, that the aforementioned results on uniqueness and existence of exterior fields apply equally in the general case.