Ellipsoidal configurations in the de Sitter spacetime

TL;DR

This paper investigates how the cosmological constant influences the equilibrium and rotational properties of large, homogeneous ellipsoidal astrophysical objects, revealing new stable configurations and bifurcation sensitivities.

Contribution

It introduces a modified tensor virial approach incorporating the cosmological constant to analyze equilibrium states of rotating ellipsoids, including triaxial configurations with minor axis rotation.

Findings

Bifurcation points are sensitive to the cosmological constant.

Triaxial equilibrium configurations are possible only with positive b.

Minor axis rotation can occur in prolate geometries with b e; it is impossible in oblate cases.

Abstract

The cosmological constant $\Lambda$ modifies certain properties of large astrophysical rotating configurations with ellipsoidal geometries, provided the objects are not too compact. Assuming an equilibrium configuration and so using the tensor virial equation with $\Lambda$ we explore several equilibrium properties of homogeneous rotating ellipsoids. One shows that the bifurcation point, which in the oblate case distinguishes the Maclaurin ellipsoid from the Jacobi ellipsoid, is sensitive to the cosmological constant. Adding to that, the cosmological constant allows triaxial configurations of equilibrium rotating the minor axis as solutions of the virial equations. The significance of the result lies in the fact that minor axis rotation is indeed found in nature. Being impossible for the oblate case, it is permissible for prolate geometries, with $\Lambda$ zero and positive. For the triaxial case, however, an equilibrium solution is found only for non-zero positive $\Lambda$. Finally, we solve the tensor virial equation for the angular velocity and display special effects of the cosmological constant there.