201 research outputs found
Geodesics around Weyl-Bach's Ring Solution
We explore some of the gravitational features of a uniform ring both in the
Newtonian potential theory and in General Relativity. We use a spacetime
associated to a Weyl static solution of the vacuum Einstein's equations with
ring like singularity. The Newtonian motion for a test particle in the
gravitational field of the ring is studied and compared with the corresponding
geodesic motion in the given spacetime. We have found a relativistic peculiar
attraction: free falling particle geodesics are lead to the inner rim but never
hit the ring.Comment: 8 figures, 14 pages. LaTeX w/ subfigure, graphic
Exact General Relativistic Thick Disks
A method to construct exact general relativistic thick disks that is a simple
generalization of the ``displace, cut and reflect'' method commonly used in
Newtonian, as well as, in Einstein theory of gravitation is presented. This
generalization consists in the addition of a new step in the above mentioned
method. The new method can be pictured as a ``displace, cut, {\it fill} and
reflect'' method. In the Newtonian case, the method is illustrated in some
detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable
physical properties. In the relativistic case two solutions of the Weyl
equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the
Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild
metric in isotropic coordinates is employed to construct another family of
thick disks. In all the considered cases we have non trivial ranges of the
involved parameter that yield thick disks in which all the energy conditions
are satisfied.Comment: 11 pages, RevTex, 9 eps figs. Accepted for publication in PR
On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure
We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo
solution of the Einstein Equations in terms of bars. We find that each
multi-pole correspond to the Newtonian potential of a bar with linear density
proportional to a Legendre Polynomial. We use this fact to find an integral
representation of the function. These integral representations are
used in the context of the inverse scattering method to find solutions
associated to one or more rotating bodies each one with their own multi-polar
structure.Comment: To be published in Classical and Quantum Gravit
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
General-relativistic Model of Magnetically Driven Jet
The general scheme for the construction of the general-relativistic model of
the magnetically driven jet is suggested. The method is based on the usage of
the 3+1 MHD formalism. It is shown that the critical points of the flow and the
explicit radial behavior of the physical variables may be derived through the
jet ``profile function."Comment: 12 pages, LaTex, no figure
Multi-Black-Holes in Three Dimensions
We construct time-dependent multi-centre solutions to three-dimensional
general relativity with zero or negative cosmological constant. These solutions
correspond to dynamical systems of freely falling black holes and conical
singularities, with a multiply connected spacetime topology. Stationary
multi-black-hole solutions are possible only in the extreme black hole case.Comment: 8 pages, \LaTex, 4 figures (available on request), GCR 94/02/0
Quantum singularities in a model of f(R) Gravity
The formation of a naked singularity in a model of f(R) gravity having as
source a linear electromagnetic field is considered in view of quantum
mechanics. Quantum test fields obeying the Klein-Gordon, Dirac and Maxwell
equations are used to probe the classical timelike naked singularity developed
at r=0. We prove that the spatial derivative operator of the fields fails to be
essentially self-adjoint. As a result, the classical timelike naked singularity
remains quantum mechanically singular when it is probed with quantum fields
having different spin structures.Comment: 12 pages, final version. Accepted for publication in EPJ
On the stability of general relativistic geometric thin disks
The stability of general relativistic thin disks is investigated under a
general first order perturbation of the energy momentum tensor. In particular,
we consider temporal, radial and azimuthal "test matter" perturbations of the
quantities involved on the plane . We study the thin disks generated by
applying the "displace, cut and reflect" method, usually known as the image
method, to the Schwarzschild metric in isotropic coordinates and to the
Chazy-Curzon metric and the Zipoy-Voorhees metric (-metric) in Weyl
coordinates. In the case of the isotropic Schwarzschild thin disk, where a
radial pressure is present to support the gravitational attraction, the disk is
stable and the perturbation favors the formation of rings. Also, we found the
expected result that the thin disk models generated by the Chazy-Curzon and
Zipoy-Voorhees metric with only azimuthal pressure are not stable under a
general first order perturbationComment: 11 pages, RevTex. Phys Rev D (in press
An infinite family of magnetized Morgan-Morgan relativistic thin disks
Applying the Horsk\'y-Mitskievitch conjecture to the empty space solutions of
Morgan and Morgan due to the gravitational field of a finite disk, we have
obtained the corresponding solutions of the Einstein-Maxwell equations. The
resulting expressions are simply written in terms of oblate spheroidal
coordinates and the solutions represent fields due to magnetized static thin
disk of finite extension. Now, although the solutions are not asymptotically
flat, the masses of the disks are finite and the energy-momentum tensor agrees
with the energy conditions. Furthermore, the magnetic field and the circular
velocity show an acceptable physical behavior.Comment: Submitted to IJTP. This paper is a revised and extended version of a
paper that was presented at arXiv:1006.203
Gravitational hedgehog, stringy hedgehog and stringy sphere
We investigate the solutions of Einstein equations such that a hedgehog
solution is matched to different exterior or interior solutions via a spherical
shell. In the case where both the exterior and the interior regions are
hedgehog solutions or one of them is flat, the resulting spherical shell
becomes a stringy shell. We also consider more general matchings and see that
in this case the shell deviates from its stringy character.Comment: 11 page
- …