10,055 research outputs found
On Multipolar Analytical Potentials for Galaxies
We present analytical potential-density pairs in three dimensions for the
gravitational field of galaxies, obtained by thickening the multipolar
expansion up to the quadrupole term. These may be interpreted as
generalizations of the Miyamoto and Nagai potential-density pairs. With a
suitable restriction on the possible values of the multipole moments, the
density distributions are positive and monotone decreasing functions of the
radial and axial coordinates
A General Relativistic Model for the Gravitational Field of Active Galactic Nuclei Surrounded by a Disk
An exact but simple general relativistic model for the gravitational field of
active galactic nuclei is constructed, based on the superposition in Weyl
coordinates of a black hole, a Chazy-Curzon disk and two rods, which represent
matter jets. The influence of the rods on the matter properties of the disk and
on its stability is examined. We find that in general they contribute to
destabilize the disk. Also the oscillation frequencies for perturbed circular
geodesics on the disk are computed, and some geodesic orbits for the superposed
metric are numerically calculated.Comment: 24 pages, LATEX. Phys. Rev. D (in press
Relativistic Models of Galaxies
A special form of the isotropic metric in cylindrical coordinates is used to
construct what may be interpreted as the General Relativistic versions of some
wellknown potential-density pairs used in Newtonian gravity to model
three-dimensional distributions of matter in galaxies. The components of the
energy-momentum tensor are calculated for the first two Miyamoto-Nagai
potentials and a particular potential due to Satoh. The three potentials yield
distributions of matter in which all tensions are pressures and all energy
conditions are satisfied for certain ranges of the free parameters. A few
non-planar geodesic orbits are computed for one of the potentials and compared
with the Newtonian case. Rotation is also incorporated to the models and the
effects of the source rotation on the rotation profile are calculated as first
order corrections by using an approximate form of the Kerr metric in isotropic
coordinates.Comment: 18 pages, 23 eps figures, uses mn2e.cls style file, to be published
in MNRA
Newtonian and General Relativistic Models of Spherical Shells
A family of spherical shells with varying thickness is derived by using a
simple Newtonian potential-density pair. Then, a particular isotropic form of a
metric in spherical coordinates is used to construct a General Relativistic
version of the Newtonian family of shells. The matter of these relativistic
shells presents equal azimuthal and polar pressures, while the radial pressure
is a constant times the tangential pressure. We also make a first study of
stability of both the Newtonian and relativistic families of shells.Comment: 13 pages, 5 figures, accepted for publication in MNRA
Exact General Relativistic Discs and the Advance of Perihelion
The advance of perihelion for geodesic motion on the galactic plane of some
exact general relativistic disc solutions is calculated. Approximate analytical
and numerical results are presented for the static Chazy-Curzon and the
Schwarzschild discs in Weyl coordinates, the Schwarzschid disc in isotropic
coordinantes and the stationary Kerr disc in the Weyl-Lewis-Papapetrou metrics.
It is found that for these disc models the advance of perihelion may be an
increasing or decreasing function of the orbital excentricity. The precession
due to Newtonian gravity for these disc models is also calculated.Comment: 11 pages, 8 figure
The need for dark matter in galaxies
Cooperstock and Tieu have proposed a model to account for galactic rotation
curves without invoking dark matter. I argue that no model of this type can
work
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