Conformally Flat Noncircular Spacetimes

Abstract

The general metric for conformally flat stationary cyclic symmetric noncircular spacetimes is explicitly given. In spite of the complexity introduced by the inclusion of noncircular contributions, the related metric is derived via the full integration of the conformal flatness constraints. It is also shown that the conditions for the existence of a rotation axis (axisymmetry) are the same ones which restrict the above class of spacetimes to be static. As a consequence, a known theorem by Collinson is just part of a more general result: any conformally flat stationary cyclic symmetric spacetime, even a noncircular one, is additionally axisymmetric if and only if it is also static. Since recent astrophysical motivations point in the direction of considering noncircular configurations to describe magnetized neutron stars, the above results seem to be relevant in this context.

7 pages

References in corpus (4)

• Relativistic stars with poloidal and toroidal magnetic fields and meridional flow
• Grad-Shafranov equation in noncircular stationary axisymmetric spacetimes
• Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium
• Comment on "Conformally flat stationary axisymmetric metrics"

Cited by in corpus (6)

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• Parameterizations of black-hole spacetimes beyond circularity
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• Resonant orbits of rotating black holes beyond circularity: Discontinuity along parameter shift
• Epicyclic oscillations of charged particles in stationary solutions immersed in a magnetic field with application to the Kerr--Newman black hole
• On the Residual Symmetries of the Gravitational Field