Ellipsoidal shapes in general relativity: general definitions and an application

Details Ellipsoidal shapes in general relativity: general definitions and an application Ellipsoidal shapes in general relativity: general definitions and an application

2003-01-07

arxiv.org/abs/gr-qc/0301019v2

Class.Quant.Grav. 20 (2003) 2855

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 22 pages, Revised version accepted in Class. Quantum. Grav., references added

Scientific paper

10.1088/0264-9381/20/13/330

A generalization of the notion of ellipsoids to curved Riemannian spaces is given and the possibility to use it in describing the shapes of rotating bodies in general relativity is examined. As an illustrative example, stationary, axisymmetric perfect-fluid spacetimes with a so-called confocal inside ellipsoidal symmetry are investigated in detail under the assumption that the 4-velocity of the fluid is parallel to a time-like Killing vector field. A class of perfect-fluid metrics representing interior NUT-spacetimes is obtained along with a vacuum solution with a non-zero cosmological constant.

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