A source of a quasi--spherical space--time: The case for the M--Q solution

Abstract

We present a physically reasonable source for an static, axially--symmetric solution to the Einstein equations. Arguments are provided, supporting our belief that the exterior space--time produced by such source, describing a quadrupole correction to the Schwarzschild metric, is particularly suitable (among known solutions of the Weyl family) for discussing the properties of quasi--spherical gravitational fields.

arXiv comment34 pages, 9 figures. To appear in GRG

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• Self-similarity in static axially symmetric relativistic fluids
• Geodesics in the linearized multipole solution: Distinguishing black holes from naked singularities
• Approximate gravitational field of a rotating deformed mass
• A general relativistic effect in quasi-spherical objects as the possible origin of relativistic jets
• Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations