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

Collapsing Spheres Satisfying An "Euclidean Condition"

We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all models are necessarily geodesic and a subclass of the Lemaitre-Tolman-Bondi solution is obtained. In the dissipative case solutions are non-geodesic and are characterized by the fact that all non-gravitational forces acting on any fluid element produces a radial three-acceleration independent on its inertial mass.Comment: 1o pages, Latex. Title changed and text shortened to fit the version to appear in Gen.Rel.Grav

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

Static cylindrical symmetry and conformal flatness

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime. It is shown that the conformally flat solution with equal principal stresses represents an incompressible fluid. It is also proved that any conformally flat cylindrically symmetric static source cannot be matched through Darmois conditions to the Levi-Civita spacetime. Further evidence is given that when the Newtonian mass per unit length reaches 1/2 the spacetime has plane symmetry.Comment: 13 pages, Late

Measuring multipole moments of Weyl metrics by means of gyroscopes

Using the technique of Rindler and Perlick we calculate the total precession per revolution of a gyroscope circumventing the source of Weyl metrics. We establish thereby a link between the multipole moments of the source and an ``observable'' quantity. Special attention deserves the case of the gamma-metric. As an extension of this result we also present the corresponding expressions for some stationary space-times.Comment: 18 pages Latex, To appear in J.Math.Phy

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

Radiating Shear-Free Gravitational Collapse with Charge

We present a new shear free model for the gravitational collapse of a spherically symmetric charged body. We propose a dissipative contraction with radiation emitted outwards. The Einstein field equations, using the junction conditions and an ansatz, are integrated numerically. A check of the energy conditions is also performed. We obtain that the charge delays the black hole formation and it can even halt the collapse.Comment: 22 pages, 9 figures. It has been corrected several typos and included several references. Accepted for publication in GR

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

Dynamics of Non-adiabatic Charged Cylindrical Gravitational Collapse

This paper is devoted to study the dynamics of gravitational collapse in the Misner and Sharp formalism. We take non-viscous heat conducting charged anisotropic fluid as a collapsing matter with cylindrical symmetry. The dynamical equations are derived and coupled with the transport equation for heat flux obtained from the M$\ddot{u}$ller-Israel-Stewart causal thermodynamic theory. We discuss the role of anisotropy, electric charge and radial heat flux over the dynamics of the collapse with the help of coupled equation.Comment: 15 pages, accepted for publication in Astrophys. Space Sc

Emergence and persistence of communities in coevolutionary networks

We investigate the emergence and persistence of communities through a recently proposed mechanism of adaptive rewiring in coevolutionary networks. We characterize the topological structures arising in a coevolutionary network subject to an adaptive rewiring process and a node dynamics given by a simple voterlike rule. We find that, for some values of the parameters describing the adaptive rewiring process, a community structure emerges on a connected network. We show that the emergence of communities is associated to a decrease in the number of active links in the system, i.e. links that connect two nodes in different states. The lifetime of the community structure state scales exponentially with the size of the system. Additionally, we find that a small noise in the node dynamics can sustain a diversity of states and a community structure in time in a finite size system. Thus, large system size and/or local noise can explain the persistence of communities and diversity in many real systems.Comment: 6 pages, 5 figures, Accepted in EPL (2014