Approximate gravitational field of a rotating deformed mass

A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters representing the quadrupole and the angular momentum respectively. The main feature of the solution is a suitable description of small deviations from spherical symmetry through perturbations of the static configuration and the massive multipole structure by using those parameters. This quality of the solution might eventually provide relevant differences with respect to the description provided by the Kerr solution.Comment: 16 pages. Latex. To appear in General Relativity and Gravitatio

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

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.Comment: 34 pages, 9 figures. To appear in GR

Non-spherical sources of static gravitational fields: investigating the boundaries of the no-hair theorem

A new, globally regular model describing a static, non spherical gravitating object in General Relativity is presented. The model is composed by a vacuum Weyl--Levi-Civita special field - the so called gamma metric - generated by a regular static distribution of mass-energy. Standard requirements of physical reasonableness such as, energy, matching and regularity conditions are satisfied. The model is used as a toy in investigating various issues related to the directional behavior of naked singularities in static spacetimes and the blackhole (Schwarschild) limit.Comment: 10 pages, 2 figure

Periastron shift in Weyl class spacetimes

The periastron position advance for geodesic motion in axially symmetric solutions of the Einstein field equations belonging to the Weyl class of vacuum solutions is investigated. Explicit examples corresponding to either static solutions (single Chazy-Curzon, Schwarzschild and a pair of them), or stationary solution (single rotating Chazy-Curzon and Kerr black hole) are discussed. The results are then applied to the case of S2-SgrA$^*$ binary system of which the periastron position advance will be soon measured with a great accuracy.Comment: To appear on General Relativity and Gravitation, vol. 37, 200

Geodesics in a quasispherical spacetime: A case of gravitational repulsion

Geodesics are studied in one of the Weyl metrics, referred to as the M--Q solution. First, arguments are provided, supporting our belief that this space--time is the more suitable (among the known solutions of the Weyl family) for discussing the properties of strong quasi--spherical gravitational fields. Then, the behaviour of geodesics is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry. Particular attention deserves the change of sign in proper radial acceleration of test particles moving radially along symmetry axis, close to the $r=2M$ surface, and related to the quadrupole moment of the source.Comment: 30 pages late

The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy

We calculate the instantaneous proper radial acceleration of test particles (as measured by a locally defined Lorentzian observer) in a Weyl spacetime, close to the horizon. As expected from the Israel theorem, there appear some bifurcations with respect to the spherically symmetric case (Schwarzschild), which are explained in terms of the behaviour of the superenergy, bringing out the physical relevance of this quantity in the study of general relativistic systems.Comment: 14 pages, Latex. 4 figures. New references added. Typos corrected. To appear in Int. J. Theor. Phy