Ellipsoidal configurations in the de Sitter spacetime

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.

15 pages, 11 figures, published in Class. Quant. Grav. References added

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• Astrophysical Configurations with Background Cosmology: Probing Dark Energy at Astrophysical Scales
• On the Magnitude of Dark Energy Voids and Overdensities
• Equilibrium configurations of fluids and their stability in higher dimensions
• Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes
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• Galactic cluster winds in presence of a dark energy
• R3 fluids
• Galaxy clusters in presence of dark energy: a kinetic approach
• New vistas on the Laplace-Runge-Lenz vector